(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 8.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. *) (* *) (*************************************************************************) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 835, 17] NotebookDataLength[ 6723947, 149376] NotebookOptionsPosition[ 6681450, 148070] NotebookOutlinePosition[ 6681843, 148087] CellTagsIndexPosition[ 6681800, 148084] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["VisibLie_E8: ", "Title", CellChangeTimes->{{3.543571764491667*^9, 3.543571772038542*^9}, { 3.543658659015625*^9, 3.54365866315625*^9}}], Cell[CellGroupData[{ Cell["\<\ A Theory of Everything Visualizer: With Octonion/Fano, Dynkin/Cartan, E8 Algebra/Group and Fundamental, Meson, \ Baryon & Atomic Element Particle Layers\ \>", "Subtitle"], Cell["J. Gregory Moxness", "Subtitle"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "This demonstration combines four demonstrations by the author (and \ integrates four others) which are theoretically related to an extended \ Standard Model (SM) originated by A.G. Lisi. It visualizes the math and \ physics of \"", ButtonBox["An Exceptionally Simple Theory of Everything", BaseStyle->"Hyperlink", ButtonData->{ URL["http://arxiv.org/abs/0711.0770"], None}, ButtonNote->"http://arxiv.org/abs/0711.0770"], "\". " }], "Subsection", CellID->538171866], Cell[CellGroupData[{ Cell["\<\ It starts with an interaction pane for visualizing the octonions, the Fano \ plane and its cubic. It also allows the manipulation of the 480 different \ permutations of the octonion basis. 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0.75}, ViewCenter -> { Rational[1, 2], Rational[1, 2], Rational[1, 2]}, ViewAngle -> 45 Degree}]}, Dynamic[$CellContext`i3], ImageSize -> All, Alignment -> Automatic], {{$CellContext`i3, 1, ""}, 1, 5, 1, AnimationRate -> Automatic, DisplayAllSteps -> True, DefaultDuration -> 3, AnimationRunning -> False, AppearanceElements -> { "ProgressSlider", "PlayPauseButton", "FasterSlowerButtons", "DirectionButton"}}, ControlType -> Animator, AppearanceElements -> None, DefaultBaseStyle -> "ListAnimate", DefaultLabelStyle -> "ListAnimateLabel", SynchronousUpdating -> True, Method -> {"DynamicCore" -> False, "TemplateExpand" -> True}, Bookmarks -> { "min" :> {$CellContext`i3 = 1}, "max" :> {$CellContext`i3 = 5}}], $CellContext`p3D$$ = " 3D", $CellContext`p3DTrk$$ = " 3D", $CellContext`permName$$ = "Parent", $CellContext`permTrk$$ = 0, $CellContext`perspective$$ = False, $CellContext`pGrad$$ = 0, $CellContext`physics$$ = True, $CellContext`physicsTrk$$ = True, $CellContext`plines$$ = {}, $CellContext`pListName$$ = "None", $CellContext`pSize$$ = $CellContext`nrml, $CellContext`pt$$ = { 0, 0, 0}, $CellContext`ptDD$$ = 0, $CellContext`ptDDTrk$$ = 0, $CellContext`pthPtCds$$ = "Identity", $CellContext`pthRot$$ = "Trans", $CellContext`pthRotTrk$$ = "Trans", $CellContext`ptsLoc$$ = {{1, 2}, 1}, $CellContext`ptsLocSav$$ = 0, $CellContext`ptype$$ = 2, $CellContext`q2a$$ = "UpQuark", $CellContext`q2b$$ = "DownQuarkBar", $CellContext`q3a$$ = "UpQuark", $CellContext`q3b$$ = "UpQuark", $CellContext`q3c$$ = "UpQuark", $CellContext`r0$$ = "l", $CellContext`r1$$ = 1, $CellContext`range$$ = 1.5, $CellContext`rank$$ = 8, $CellContext`rectification$$ = 0, $CellContext`rectNodes$$ = {}, $CellContext`refresh$$ = False, $CellContext`s0$$ = Overscript["L", "\[Vee]"], $CellContext`s1$$ = "HeptaHepteHeptiHexiPentiSteriRunciCantiPentellated", \ $CellContext`s2$$ = Overscript["L", "\[Vee]"], $CellContext`s3$$ = Overscript["L", "\[Vee]"], $CellContext`s4$$ = Overscript["L", "\[Vee]"], $CellContext`s5$$ = Overscript["L", "\[Vee]"], $CellContext`s6$$ = Overscript["L", "\[Vee]"], $CellContext`scale$$ = 0.54, $CellContext`selAlgebra$$ = "A1", $CellContext`selAlgebraTrk$$ = "A1", $CellContext`selCoxeter$$ = "", $CellContext`selCoxeterTrk$$ = "", $CellContext`selDynkin$$ = 1, $CellContext`selDynkinTrk$$ = 1, $CellContext`showAxes$$ = False, $CellContext`showAxesTrk$$ = False, $CellContext`showClickVerts$$ = False, $CellContext`showClickVertsTrk$$ = False, $CellContext`showClr$$ = False, $CellContext`showEdges$$ = True, $CellContext`showEdgesTrk$$ = True, $CellContext`showPartVert$$ = True, $CellContext`showPartVertTrk$$ = True, $CellContext`showPerim$$ = False, $CellContext`showPlocs$$ = False, $CellContext`showPmass$$ = False, $CellContext`showPolySurfaces$$ = True, $CellContext`showPtext$$ = True, $CellContext`showPtextTrk$$ = True, $CellContext`showPvecs$$ = False, $CellContext`showSurfaces$$ = False, $CellContext`sm$$ = 4, $CellContext`steps$$ = 5, $CellContext`stepsTrk$$ = 5, $CellContext`stowe$$ = True, $CellContext`tickNum$$ = 4, $CellContext`tlines$$ = {}, $CellContext`tT$$ = {}, \ $CellContext`ttED$$ = "ElectronConfigurationString", $CellContext`tTTrk$$ = {}, \ $CellContext`useDimLocs$$ = False, $CellContext`useDimLocsTrk$$ = False, $CellContext`V$$ = {0, Rational[1, 2] 2^Rational[-1, 2], Rational[1, 2], Rational[1, 2] 2^Rational[-1, 2], 0, Rational[-1, 2] 2^Rational[-1, 2], Rational[-1, 2], Rational[-1, 2] 2^Rational[-1, 2]}, $CellContext`verts$$ = {{-1, 0, 0, 0, 0, -3^Rational[-1, 2], 0, -Rational[2, 3]^Rational[1, 2]}, { 0, 0, -2^Rational[-1, 2], -2^Rational[-1, 2], 0, -3^Rational[-1, 2], 2^Rational[-1, 2], 6^Rational[-1, 2]}, { 0, 0, 2^Rational[-1, 2], 2^Rational[-1, 2], 1, 0, 0, 0}, { 0, 1, 0, 0, 0, -3^Rational[-1, 2], -2^Rational[-1, 2], 6^ Rational[-1, 2]}}, $CellContext`view3D$$ = False, $CellContext`vLineColors$$ = {}, $CellContext`vlines$$ = {}, \ $CellContext`vOverlapColor$$ = False, $CellContext`xy$$ = {1, 1}, $CellContext`XY$$ = {20, 20, 20}, $CellContext`xyVwPnt$$ = {0.75, 0.75}, $CellContext`Z$$ = {-2^Rational[-1, 2], Rational[1, 2], 0, Rational[-1, 2], -2^Rational[-1, 2], Rational[-1, 2], 0, Rational[1, 2]}, $CellContext`zoom$$ = 0, $CellContext`zVwPnt$$ = 0.75, $CellContext`zz$$ = 1, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`refresh$$], True}, 0}, {{ Hold[$CellContext`interactionPane$$], "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer"}, { "1) Math: Numbers: Octonion Fano Plane & Cubic", "2) Math: Geometry: Dynkin Diagram Algebra Creator", "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer", "4) Physics: Particle: Fundamental Quantum Element Builder", "5) Physics: Nuclear: Meson Particle Selector", "6) Physics: Atomic: Baryon Particle Selector", "7) Chemistry: Periodic Table Element Selector", "8) Biology: Life: nD 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Length[$CellContext`elines$$]], " trialities=", Dynamic[ Length[$CellContext`tlines$$]], " clicked edges=", Dynamic[ Length[ If[$CellContext`physics$$, $CellContext`plines$$, \ $CellContext`vlines$$]]]}], Row[{"axes ", Checkbox[ Dynamic[$CellContext`showAxes$$]], " edges ", Checkbox[ Dynamic[$CellContext`showEdges$$]], " physics ", Checkbox[ Dynamic[$CellContext`physics$$]], " labels ", Checkbox[ Dynamic[$CellContext`showPtext$$]], " axes locators ", Checkbox[ Dynamic[$CellContext`useDimLocs$$]], " ", RadioButtonBar[ Dynamic[$CellContext`p3D$$], {" 2D", " 3D"}], " triality ", TogglerBar[ Dynamic[$CellContext`tT$$], { "T1", "T1p", "T2", "T2p", "T4", "T4p"}], "", " steps ", Slider[ Dynamic[$CellContext`steps$$], {1, 60, 1}, ImageSize -> 60, ContinuousAction -> False], Dynamic[$CellContext`steps$$]}]}], "4) Physics: Particle: Fundamental Quantum Element Builder" -> Grid[{{" anti", "pType", "spin", "color", "gen", "row"}, { Checkbox[ Dynamic[$CellContext`anti$$]], RadioButtonBar[ Dynamic[$CellContext`ptype$$], {1, 2}], Dynamic[ SetterBar[ Dynamic[$CellContext`s0$$], $CellContext`spList, Enabled -> If[$CellContext`r1$$ == 3, False, True]]], Dynamic[ SetterBar[ Dynamic[$CellContext`c0$$], Part[$CellContext`colorList, Span[5, 8]], Enabled -> If[ Or[$CellContext`r1$$ == 1, $CellContext`r1$$ == 5], False, True]]], Dynamic[ SetterBar[ Dynamic[$CellContext`g0$$], Range[3], Enabled -> If[$CellContext`r1$$ > 2, False, True]]], Dynamic[ PopupMenu[ Dynamic[$CellContext`r0$$], $CellContext`flavorRows]]}}], "5) Physics: Nuclear: Meson Particle Selector" -> Grid[{{"quark", SetterBar[ Dynamic[$CellContext`c2a$$], {"r", "g", "b"}], SetterBar[ Dynamic[$CellContext`s2$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}], RadioButtonBar[ Dynamic[$CellContext`q2a$$], { "UpQuark" -> "u", "DownQuark" -> "d", "StrangeQuark" -> "s", "CharmQuark" -> "c", "BottomQuark" -> "b", "TopQuark" -> "t"}]}, {"antiquark", SetterBar[ Dynamic[$CellContext`c2a$$], {"r", "g", "b"}], SetterBar[ Dynamic[$CellContext`s3$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}], RadioButtonBar[ Dynamic[$CellContext`q2b$$], { "UpQuarkBar" -> "\!\(\*OverscriptBox[\(u\), \(_\)]\)", "DownQuarkBar" -> "\!\(\*OverscriptBox[\(d\), \(_\)]\)", "StrangeQuarkBar" -> "\!\(\*OverscriptBox[\(s\), \(_\)]\)", "CharmQuarkBar" -> "\!\(\*OverscriptBox[\(c\), \(_\)]\)", "BottomQuarkBar" -> "\!\(\*OverscriptBox[\(b\), \(_\)]\)", "TopQuarkBar" -> "\!\(\*OverscriptBox[\(t\), \(_\)]\)"}]}}], "6) Physics: Atomic: Baryon Particle Selector" -> Column[{ Row[{"r ", Item[ SetterBar[ Dynamic[$CellContext`s4$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}]], RadioButtonBar[ Dynamic[$CellContext`q3a$$], { "UpQuark" -> "u", "DownQuark" -> "d", "StrangeQuark" -> "s", "CharmQuark" -> "c", "BottomQuark" -> "b", 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Hold[$CellContext`scale$$], 0.54}, 0}, {{ Hold[$CellContext`cylR$$], 0.026}, 0}, {{ Hold[$CellContext`tickNum$$], 4}, 0}, {{ Hold[$CellContext`range$$], 1.5}, 0}, {{ Hold[$CellContext`limitToRange$$], True}, 0}, {{ Hold[$CellContext`pt$$], {0, 0, 0}}, 0}, {{ Hold[$CellContext`zoom$$], 0}, 0}, {{ Hold[$CellContext`favorite$$], 3}, 0}, {{ Hold[$CellContext`pGrad$$], 0}, 0}, {{ Hold[$CellContext`face$$], 1}, 0}, {{ Hold[$CellContext`auxData$$], False}, 0}, {{ Hold[$CellContext`showAxes$$], False}, 0}, {{ Hold[$CellContext`showPartVert$$], True}, 0}, {{ Hold[$CellContext`showEdges$$], True}, 0}, {{ Hold[$CellContext`showSurfaces$$], False}, 0}, {{ Hold[$CellContext`showPolySurfaces$$], True}, 0}, {{ Hold[$CellContext`showPvecs$$], False}, 0}, {{ Hold[$CellContext`showPtext$$], True}, 0}, {{ Hold[$CellContext`showPlocs$$], False}, 0}, {{ Hold[$CellContext`showPmass$$], False}, 0}, {{ Hold[$CellContext`showPerim$$], False}, 0}, {{ Hold[$CellContext`eGrad$$], 44}, 0}, {{ Hold[$CellContext`edgeVals$$], {{"All", 6}}}, 0}, {{ Hold[$CellContext`anim8EdgeList$$], False}, 0}, {{ Hold[$CellContext`eColorPos$$], True}, 0}, {{ Hold[$CellContext`eSteps$$], 1}, 0}, {{ Hold[$CellContext`eWnd$$], 100}, 0}, {{ Hold[$CellContext`innerMag$$], 0}, 0}, {{ Hold[$CellContext`dimTrim$$], 8}, 0}, {{ Hold[$CellContext`XY$$], {20, 20, 20}}, 0}, {{ Hold[$CellContext`tT$$], {}}, 0}, {{ Hold[$CellContext`showClr$$], False}, 0}, {{ Hold[$CellContext`showClickVerts$$], False}, 0}, {{ Hold[$CellContext`vOverlapColor$$], False}, 0}, {{ Hold[$CellContext`ltps$$], {}}, 0}, {{ Hold[$CellContext`physics$$], True}, 0}, {{ Hold[$CellContext`useDimLocs$$], False}, 0}, {{ Hold[$CellContext`dlXs$$], $CellContext`dls[{1}]}, 0}, {{ Hold[$CellContext`dlYs$$], $CellContext`dls[{2}]}, 0}, {{ Hold[$CellContext`dlZs$$], $CellContext`dls[{3}]}, 0}, {{ Hold[$CellContext`xy$$], {1, 1}}, 0}, {{ Hold[$CellContext`zz$$], 1}, 0}, {{ Hold[$CellContext`xyVwPnt$$], {0.75, 0.75}}, 0}, {{ Hold[$CellContext`zVwPnt$$], 0.75}, 0}, {{ Hold[$CellContext`steps$$], 5}, 0}, {{ Hold[$CellContext`nDcamera$$], 1.}, 0}, {{ Hold[$CellContext`perspective$$], False}, 0}, {{ Hold[$CellContext`pthRot$$], "Trans"}, 0}, {{ Hold[$CellContext`pthPtCds$$], "Identity"}, 0}, {{ Hold[$CellContext`ds$$], 3}, 0}, {{ Hold[$CellContext`pSize$$], $CellContext`nrml}, 0}, {{ Hold[$CellContext`pListName$$], "None"}, 0}, {{ Hold[$CellContext`dsName$$], "physics"}, 0}, {{ Hold[$CellContext`p3D$$], " 2D"}, 0}, {{ Hold[$CellContext`infile$$], "./auxData.m"}, 0}, {{ Hold[$CellContext`auxFile$$], "./auxData.xls"}, 0}, {{ Hold[$CellContext`fileOut$$], False}, 0}, {{ Hold[$CellContext`outFileDir$$], "./"}, 0}, {{ Hold[$CellContext`outFile$$], "E8out"}, 0}, {{ Hold[$CellContext`outFileType$$], ".png"}, 0}, {{ Hold[$CellContext`H$$], {0, 0, 0, 0, 0, 0, 0, 0}}, 0}, {{ Hold[$CellContext`V$$], {0, 0, 0, 0, 0, 0, 0, 0}}, 0}, {{ Hold[$CellContext`Z$$], {0, 0, 0, 0, 0, 0, 0, 0}}, 0}, {{ Hold[$CellContext`selCoxeter$$], ""}, 0}, {{ Hold[$CellContext`bAND$$], 1}, 0}, {{ Hold[$CellContext`bAND1Name$$], "Hydrogen"}, 0}, {{ Hold[$CellContext`bAND2Name$$], ""}, 0}, {{ Hold[$CellContext`fltrdSubPlot$$], CompressedData[" 1:eJwd0wOfEAYAxuEue7Va1lXbsm1zC5ddl3XZ5rK11dJybbll27Zt20+9v//z Ed7A4DZBIQGhLOB7oUIThrCEIzwRiEgkIhOFqEQjOj8Qg5j8SCxi8xNxiEs8 4pOAhCQiMUlISjICSU4KUvIzv/ArqUhNGtKSjvRkICOZyEwWspKN7OQgJ7nI TR7yko/8FKAghShMEYpSjOKUoCSlKE0ZyvIbv1OO8lSgIkFUojJVqEo1qlOD mtSiNnWoSz3q04BgGtKIxjShKc1oTgta0orWhNCGtrSjPR3oSCc604WudKM7 PehJL3rTh770oz8DGMggBvMHQxjKMIYzgpGMYjRjGMs4xjOBiUxiMlP4k7+Y yjT+ZjozmMksZvMPc5jLPOazgIUsYjFL+Jf/WMoylrOClaxiNWv4n7WsYz0b 2MgmNrOFrWxjOzvYyS52s4e97GM/BzjIIQ5zhKMc4zgnOMkpTnOGs5zjPBe4 yCUuc4WrXOM6N7jJLW5zh7vc4z4PeMgjHvOEpzzjOS94ySte84a3vOM9H/jI Jz7zhW/n/wqYtIE2 "]}, 0}, {{ Hold[$CellContext`fullVerts$$], {}}, 0}, {{ Hold[$CellContext`verts$$], {}}, 0}, {{ Hold[$CellContext`rectification$$], 0}, 0}, {{ Hold[$CellContext`tlines$$], {}}, 0}, {{ Hold[$CellContext`elines$$], {}}, 0}, {{ Hold[$CellContext`plines$$], {}}, 0}, {{ Hold[$CellContext`vlines$$], {}}, 0}, {{ Hold[$CellContext`vLineColors$$], {}}, 0}, {{ Hold[$CellContext`fa$$], {}}, 0}, {{ Hold[$CellContext`fp$$], {}}, 0}, {{ Hold[$CellContext`fc$$], {}}, 0}, {{ Hold[$CellContext`fs$$], {}}, 0}, {{ Hold[$CellContext`fg$$], {}}, 0}, {{ Hold[$CellContext`fr$$], {}}, 0}, {{ Hold[$CellContext`edgeList$$], {{0, 0}, {"All", 6}}}, 0}, {{ Hold[$CellContext`newPTcd$$], {}}, 0}, {{ Hold[$CellContext`lastViewPoint$$], {1.3, 2.4, 2.}}, 0}, {{ Hold[$CellContext`locPtCdArr$$], {{0, 0}, {0, 0}, {0, 0}, {0, 0}, { 0, 0}, {0, 0}, {0, 0}, {0, 0}}}}, {{ Hold[$CellContext`dispArr$$], { "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?"}}, 0}, {{ Hold[$CellContext`rectNodes$$], {}}, 0}, {{ Hold[$CellContext`eLim$$], 100}, 0}, {{ Hold[$CellContext`edgeMag$$], 1}, 0}, {{ Hold[$CellContext`eSort$$], {}}, 0}, {{ Hold[$CellContext`eVs$$], {}}, 0}, {{ Hold[$CellContext`eVF$$], {}}, 0}, {{ Hold[$CellContext`lie$$], ""}, 0}, {{ Hold[$CellContext`dsTrk$$], 3}, 0}, {{ Hold[$CellContext`fltrdSubPlotTrk$$], CompressedData[" 1:eJwd0wOfEAYAxuEue7Va1lXbsm1zC5ddl3XZ5rK11dJybbll27Zt20+9v//z Ed7A4DZBIQGhLOB7oUIThrCEIzwRiEgkIhOFqEQjOj8Qg5j8SCxi8xNxiEs8 4pOAhCQiMUlISjICSU4KUvIzv/ArqUhNGtKSjvRkICOZyEwWspKN7OQgJ7nI TR7yko/8FKAghShMEYpSjOKUoCSlKE0ZyvIbv1OO8lSgIkFUojJVqEo1qlOD mtSiNnWoSz3q04BgGtKIxjShKc1oTgta0orWhNCGtrSjPR3oSCc604WudKM7 PehJL3rTh770oz8DGMggBvMHQxjKMIYzgpGMYjRjGMs4xjOBiUxiMlP4k7+Y yjT+ZjozmMksZvMPc5jLPOazgIUsYjFL+Jf/WMoylrOClaxiNWv4n7WsYz0b 2MgmNrOFrWxjOzvYyS52s4e97GM/BzjIIQ5zhKMc4zgnOMkpTnOGs5zjPBe4 yCUuc4WrXOM6N7jJLW5zh7vc4z4PeMgjHvOEpzzjOS94ySte84a3vOM9H/jI Jz7zhW/n/wqYtIE2 "]}, 0}, {{ Hold[$CellContext`auxDataTrk$$], False}, 0}, {{ Hold[$CellContext`innerMagTrk$$], 0}, 0}, {{ Hold[$CellContext`dimTrimTrk$$], 8}, 0}, {{ Hold[$CellContext`showClickVertsTrk$$], False}, 0}, {{ Hold[$CellContext`physicsTrk$$], True}, 0}, {{ Hold[$CellContext`faceTrk$$], 1}, 0}, {{ Hold[$CellContext`bANDTrk$$], 1}, 0}, {{ Hold[$CellContext`edgeValsTrk$$], {{"All", 6}}}, 0}, {{ Hold[$CellContext`infileTrk$$], "./auxData.m"}, 0}, {{ Hold[$CellContext`bAND1NameTrk$$], ""}, 0}, {{ Hold[$CellContext`bAND2NameTrk$$], ""}, 0}, {{ Hold[$CellContext`selCoxeterTrk$$], ""}, 0}, {{ Hold[$CellContext`favoriteTrk$$], 3}, 0}, {{ Hold[$CellContext`p3DTrk$$], " 3D"}, 0}, {{ Hold[$CellContext`tTTrk$$], {}}, 0}, {{ Hold[$CellContext`locPtCdTrk$$], {{0, 0}, {0, 0}, {0, 0}, {0, 0}, { 0, 0}, {0, 0}, {0, 0}, {0, 0}}}}, {{ Hold[$CellContext`pthRotTrk$$], "Trans"}, 0}, {{ Hold[$CellContext`useDimLocsTrk$$], False}, 0}, {{ Hold[$CellContext`ltpsTrk$$], {}}, 0}, {{ Hold[$CellContext`showAxesTrk$$], False}, 0}, {{ Hold[$CellContext`showEdgesTrk$$], False}, 0}, {{ Hold[$CellContext`showPtextTrk$$], True}, 0}, {{ Hold[$CellContext`showPartVertTrk$$], True}, 0}, {{ Hold[$CellContext`stepsTrk$$], 5}, 0}, {{ Hold[$CellContext`outSav$$], "Working..."}, 0}, {{ Hold[$CellContext`more$$], True}, 0}, {{ Hold[$CellContext`anti$$], False}, 0}, {{ Hold[$CellContext`ptype$$], 2}, 0}, {{ Hold[$CellContext`r1$$], 1}, 0}, {{ Hold[$CellContext`c0$$], "w"}, 0}, {{ Hold[$CellContext`s0$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`s1$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`g0$$], 1}, 0}, {{ Hold[$CellContext`r0$$], "l"}, 0}, {{ Hold[$CellContext`q2a$$], "UpQuark"}, 0}, {{ Hold[$CellContext`s2$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`c2a$$], "r"}, 0}, {{ Hold[$CellContext`q2b$$], "DownQuarkBar"}, 0}, {{ Hold[$CellContext`s3$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`q3a$$], "UpQuark"}, 0}, {{ Hold[$CellContext`s4$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`q3b$$], "UpQuark"}, 0}, {{ Hold[$CellContext`s5$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`q3c$$], "UpQuark"}, 0}, {{ Hold[$CellContext`s6$$], Overscript["L", "\[Vee]"]}, 0}, {{ Hold[$CellContext`isotope$$], 0}, 0}, {{ Hold[$CellContext`ttED$$], "ElectronConfigurationString"}, 0}, {{ Hold[$CellContext`n0$$], 8}, 0}, {{ Hold[$CellContext`view3D$$], True}, 0}, {{ Hold[$CellContext`density$$], False}, 0}, {{ Hold[$CellContext`explode$$], 4}, 0}, {{ Hold[$CellContext`stowe$$], False}, 0}}, Typeset`size$$ = {644., {270., 276.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`interactionPane$279220$$ = 0, $CellContext`dynkTbl$279225$$ = False, $CellContext`ptsLoc$279226$$ = False, $CellContext`ptDD$279227$$ = False, $CellContext`permTrk$279228$$ = False, $CellContext`ptDDTrk$279229$$ = False}, DynamicBox[ Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`affine$$ = 0, $CellContext`affineTrk$$ = 0, $CellContext`alg$$ = "A1", $CellContext`alg1$$ = "A", $CellContext`algTrk$$ = "A1", $CellContext`altMask$$ = False, $CellContext`anim8EdgeList$$ = False, $CellContext`anti$$ = False, $CellContext`artPrint$$ = False, $CellContext`auxData$$ = False, $CellContext`auxDataTrk$$ = False, $CellContext`auxFile$$ = "./auxData.xls", $CellContext`bAND$$ = 1, $CellContext`bAND1Name$$ = "Hydrogen", $CellContext`bAND1NameTrk$$ = "", $CellContext`bAND2Name$$ = "", $CellContext`bAND2NameTrk$$ = "", $CellContext`bANDTrk$$ = 1, $CellContext`c0$$ = "w", $CellContext`c2a$$ = "r", $CellContext`cylR$$ = 0.026, $CellContext`density$$ = False, $CellContext`dimTrim$$ = 8, $CellContext`dimTrimTrk$$ = 8, $CellContext`dispArr$$ = { "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?", "?"}, $CellContext`dlXs$$ = $CellContext`dls[{ 1}], $CellContext`dlYs$$ = $CellContext`dls[{ 2}], $CellContext`dlZs$$ = $CellContext`dls[{ 3}], $CellContext`ds$$ = 3, $CellContext`dsName$$ = "physics", $CellContext`dsTrk$$ = 3, $CellContext`dynkin$$ = {}, $CellContext`dynkSav$$ = 0, $CellContext`dynkTbl$$ = {{{{1, 2}, 1}}, {}, 0}, $CellContext`eColorPos$$ = True, $CellContext`edgeList$$ = {{0, 0}, { "All", 6}}, $CellContext`edgeMag$$ = 1, $CellContext`edgeVals$$ = {{ "All", 6}}, $CellContext`edgeValsTrk$$ = {{ "All", 6}}, $CellContext`eGrad$$ = 44, $CellContext`eLim$$ = 100, $CellContext`elines$$ = {}, $CellContext`eSort$$ = {}, \ $CellContext`eSteps$$ = 1, $CellContext`eVF$$ = {}, $CellContext`eVs$$ = {}, \ $CellContext`eWnd$$ = 100, $CellContext`explode$$ = 4, $CellContext`fa$$ = {}, $CellContext`face$$ = 1, $CellContext`faceTrk$$ = 1, $CellContext`favorite$$ = 3, $CellContext`favoriteTrk$$ = 3, $CellContext`fc$$ = {}, $CellContext`fg$$ = {}, \ $CellContext`fileOnly$$ = False, $CellContext`fileOut$$ = False, $CellContext`flip$$ = True, $CellContext`fltrdSubPlot$$ = CompressedData[" 1:eJwd0wOfEAYAxuEue7Va1lXbsm1zC5ddl3XZ5rK11dJybbll27Zt20+9v//z Ed7A4DZBIQGhLOB7oUIThrCEIzwRiEgkIhOFqEQjOj8Qg5j8SCxi8xNxiEs8 4pOAhCQiMUlISjICSU4KUvIzv/ArqUhNGtKSjvRkICOZyEwWspKN7OQgJ7nI TR7yko/8FKAghShMEYpSjOKUoCSlKE0ZyvIbv1OO8lSgIkFUojJVqEo1qlOD mtSiNnWoSz3q04BgGtKIxjShKc1oTgta0orWhNCGtrSjPR3oSCc604WudKM7 PehJL3rTh770oz8DGMggBvMHQxjKMIYzgpGMYjRjGMs4xjOBiUxiMlP4k7+Y yjT+ZjozmMksZvMPc5jLPOazgIUsYjFL+Jf/WMoylrOClaxiNWv4n7WsYz0b 2MgmNrOFrWxjOzvYyS52s4e97GM/BzjIIQ5zhKMc4zgnOMkpTnOGs5zjPBe4 yCUuc4WrXOM6N7jJLW5zh7vc4z4PeMgjHvOEpzzjOS94ySte84a3vOM9H/jI Jz7zhW/n/wqYtIE2 "], $CellContext`fltrdSubPlotTrk$$ = CompressedData[" 1:eJwd0wOfEAYAxuEue7Va1lXbsm1zC5ddl3XZ5rK11dJybbll27Zt20+9v//z Ed7A4DZBIQGhLOB7oUIThrCEIzwRiEgkIhOFqEQjOj8Qg5j8SCxi8xNxiEs8 4pOAhCQiMUlISjICSU4KUvIzv/ArqUhNGtKSjvRkICOZyEwWspKN7OQgJ7nI TR7yko/8FKAghShMEYpSjOKUoCSlKE0ZyvIbv1OO8lSgIkFUojJVqEo1qlOD mtSiNnWoSz3q04BgGtKIxjShKc1oTgta0orWhNCGtrSjPR3oSCc604WudKM7 PehJL3rTh770oz8DGMggBvMHQxjKMIYzgpGMYjRjGMs4xjOBiUxiMlP4k7+Y yjT+ZjozmMksZvMPc5jLPOazgIUsYjFL+Jf/WMoylrOClaxiNWv4n7WsYz0b 2MgmNrOFrWxjOzvYyS52s4e97GM/BzjIIQ5zhKMc4zgnOMkpTnOGs5zjPBe4 yCUuc4WrXOM6N7jJLW5zh7vc4z4PeMgjHvOEpzzjOS94ySte84a3vOM9H/jI Jz7zhW/n/wqYtIE2 "], $CellContext`fp$$ = {}, $CellContext`fpC$$ = 1, $CellContext`fpG$$ = 1, $CellContext`fPi$$ = 1, $CellContext`fr$$ = {}, $CellContext`fs$$ = {}, \ $CellContext`fullVerts$$ = {}, $CellContext`g0$$ = 1, $CellContext`group$$ = "Sl(2)", $CellContext`H$$ = {0, 0, 0, 0, 0, 0, 0, 0}, $CellContext`IJKLstyle$$ = False, $CellContext`infile$$ = "./auxData.m", $CellContext`infileTrk$$ = "./auxData.m", $CellContext`init$$ = True, $CellContext`innerMag$$ = 0, $CellContext`innerMagTrk$$ = 0, $CellContext`interactionPane$$ = "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer", \ $CellContext`invMask$$ = True, $CellContext`isotope$$ = 0, $CellContext`lastViewPoint$$ = {1.3, 2.4, 2.}, $CellContext`lie$$ = "", $CellContext`limitToRange$$ = True, $CellContext`locPtCdArr$$ = {{0, 0}, {0, 0}, {0, 0}, {0, 0}, { 0, 0}, {0, 0}, {0, 0}, {0, 0}}, $CellContext`locPtCdTrk$$ = {{0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}, {0, 0}}, $CellContext`ltps$$ = {}, $CellContext`ltpsTrk$$ = {}, \ $CellContext`more$$ = True, $CellContext`n0$$ = 8, $CellContext`n1$$ = 1, $CellContext`n2$$ = 2, $CellContext`n3$$ = 3, $CellContext`nDcamera$$ = 1., $CellContext`newPTcd$$ = {}, $CellContext`octImag$$ = { Subscript[$CellContext`\[ScriptE], 1], Subscript[$CellContext`\[ScriptE], 2], Subscript[$CellContext`\[ScriptE], 3], Subscript[$CellContext`\[ScriptE], 4], Subscript[$CellContext`\[ScriptE], 5], Subscript[$CellContext`\[ScriptE], 6], Subscript[$CellContext`\[ScriptE], 7]}, $CellContext`outFile$$ = "E8out", $CellContext`outFileDir$$ = "./", $CellContext`outFileType$$ = ".png", $CellContext`outSav$$ = "Working...", $CellContext`p3D$$ = " 2D", $CellContext`p3DTrk$$ = " 3D", $CellContext`permName$$ = "Parent", $CellContext`permTrk$$ = 0, $CellContext`perspective$$ = False, $CellContext`pGrad$$ = 0, $CellContext`physics$$ = True, $CellContext`physicsTrk$$ = True, $CellContext`plines$$ = {}, $CellContext`pListName$$ = "None", $CellContext`pSize$$ = $CellContext`nrml, $CellContext`pt$$ = \ {0, 0, 0}, $CellContext`ptDD$$ = 0, $CellContext`ptDDTrk$$ = 0, $CellContext`pthPtCds$$ = "Identity", $CellContext`pthRot$$ = "Trans", $CellContext`pthRotTrk$$ = "Trans", $CellContext`ptsLoc$$ = {{1, 2}, 1}, $CellContext`ptsLocSav$$ = 0, $CellContext`ptype$$ = 2, $CellContext`q2a$$ = "UpQuark", $CellContext`q2b$$ = "DownQuarkBar", $CellContext`q3a$$ = "UpQuark", $CellContext`q3b$$ = "UpQuark", $CellContext`q3c$$ = "UpQuark", $CellContext`r0$$ = "l", $CellContext`r1$$ = 1, $CellContext`range$$ = 1.5, $CellContext`rank$$ = 1, $CellContext`rectification$$ = 0, $CellContext`rectNodes$$ = {}, $CellContext`refresh$$ = True, $CellContext`s0$$ = Overscript["L", "\[Vee]"], $CellContext`s1$$ = Overscript["L", "\[Vee]"], $CellContext`s2$$ = Overscript["L", "\[Vee]"], $CellContext`s3$$ = Overscript["L", "\[Vee]"], $CellContext`s4$$ = Overscript["L", "\[Vee]"], $CellContext`s5$$ = Overscript["L", "\[Vee]"], $CellContext`s6$$ = Overscript["L", "\[Vee]"], $CellContext`scale$$ = 0.54, $CellContext`selAlgebra$$ = "A1", $CellContext`selAlgebraTrk$$ = "A1", $CellContext`selCoxeter$$ = "", $CellContext`selCoxeterTrk$$ = "", $CellContext`selDynkin$$ = 1, $CellContext`selDynkinTrk$$ = 1, $CellContext`showAxes$$ = False, $CellContext`showAxesTrk$$ = False, $CellContext`showClickVerts$$ = False, $CellContext`showClickVertsTrk$$ = False, $CellContext`showClr$$ = False, $CellContext`showEdges$$ = True, $CellContext`showEdgesTrk$$ = False, $CellContext`showPartVert$$ = True, $CellContext`showPartVertTrk$$ = True, $CellContext`showPerim$$ = False, $CellContext`showPlocs$$ = False, $CellContext`showPmass$$ = False, $CellContext`showPolySurfaces$$ = True, $CellContext`showPtext$$ = True, $CellContext`showPtextTrk$$ = True, $CellContext`showPvecs$$ = False, $CellContext`showSurfaces$$ = False, $CellContext`sm$$ = 4, $CellContext`steps$$ = 5, $CellContext`stepsTrk$$ = 5, $CellContext`stowe$$ = False, $CellContext`tickNum$$ = 4, $CellContext`tlines$$ = {}, $CellContext`tT$$ = {}, \ $CellContext`ttED$$ = "ElectronConfigurationString", $CellContext`tTTrk$$ = {}, \ $CellContext`useDimLocs$$ = False, $CellContext`useDimLocsTrk$$ = False, $CellContext`V$$ = {0, 0, 0, 0, 0, 0, 0, 0}, $CellContext`verts$$ = {}, $CellContext`view3D$$ = True, $CellContext`vLineColors$$ = {}, $CellContext`vlines$$ = {}, \ $CellContext`vOverlapColor$$ = False, $CellContext`xy$$ = {1, 1}, $CellContext`XY$$ = {20, 20, 20}, $CellContext`xyVwPnt$$ = {0.75, 0.75}, $CellContext`Z$$ = {0, 0, 0, 0, 0, 0, 0, 0}, $CellContext`zoom$$ = 0, $CellContext`zVwPnt$$ = 0.75, $CellContext`zz$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`interactionPane$$, \ $CellContext`interactionPane$279220$$, 0], Hold[$CellContext`dynkTbl$$, $CellContext`dynkTbl$279225$$, False], Hold[$CellContext`ptsLoc$$, $CellContext`ptsLoc$279226$$, False], Hold[$CellContext`ptDD$$, $CellContext`ptDD$279227$$, False], Hold[$CellContext`permTrk$$, $CellContext`permTrk$279228$$, False], Hold[$CellContext`ptDDTrk$$, $CellContext`ptDDTrk$279229$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Pane[ Switch[$CellContext`interactionPane$$, Part[$CellContext`pdList, 1], $CellContext`doFano, Part[$CellContext`pdList, 2], $CellContext`doDynkin, Part[$CellContext`pdList, 3], $CellContext`doE8, Part[$CellContext`pdList, 4], $CellContext`doParticle, Part[$CellContext`pdList, 5], $CellContext`doMeson, Part[$CellContext`pdList, 6], $CellContext`doBaryon, Part[$CellContext`pdList, 7], $CellContext`doAtom, Part[$CellContext`pdList, 8], $CellContext`doHMI]], "Specifications" :> {{{$CellContext`refresh$$, True}, 0, ControlType -> None, ControlPlacement -> Left}, {{$CellContext`interactionPane$$, "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer"}, { "1) Math: Numbers: Octonion Fano Plane & Cubic", "2) Math: Geometry: Dynkin Diagram Algebra Creator", "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer", "4) Physics: Particle: Fundamental Quantum Element Builder", "5) Physics: Nuclear: Meson Particle Selector", "6) Physics: Atomic: Baryon Particle Selector", "7) Chemistry: Periodic Table Element Selector", "8) Biology: Life: nD Human Machine Interface"}, ControlType -> PopupMenu}, Item[ PaneSelector[{ "1) Math: Numbers: Octonion Fano Plane & Cubic" -> Column[{ Row[{"Fano basis permutation: sm_anti ", Checkbox[ Dynamic[$CellContext`invMask$$]], " sm_type[yaw_spin] ", RadioButtonBar[ Dynamic[$CellContext`altMask$$], {False -> 1, True -> 2}], Dynamic[ If[$CellContext`altMask$$, " In ", " Out"]], " sm_spin ", Dynamic[ SetterBar[ Dynamic[$CellContext`sm$$], {1 -> Part[ $CellContext`smCnv[$CellContext`altMask$$], 1], 2 -> Part[ $CellContext`smCnv[$CellContext`altMask$$], 2], 3 -> Part[ $CellContext`smCnv[$CellContext`altMask$$], 3], 4 -> Part[ $CellContext`smCnv[$CellContext`altMask$$], 4]}]], Dynamic[ $CellContext`smQ[ Part[ $CellContext`smCnv[$CellContext`altMask$$], \ $CellContext`sm$$]]], Dynamic[ Part[$CellContext`spList, $CellContext`sm$$]], "\[RightArrow]", Dynamic[ $CellContext`hexMask[$CellContext`invMask$$, \ $CellContext`altMask$$, $CellContext`fPi$$, $CellContext`sm$$]], " fp_color ", Dynamic[ SetterBar[ Dynamic[$CellContext`fpC$$], {0 -> Part[ Part[$CellContext`colorList, Span[5, 8]], 1], 1 -> Part[ Part[$CellContext`colorList, Span[5, 8]], 2], 2 -> Part[ Part[$CellContext`colorList, Span[5, 8]], 3], 3 -> Part[ Part[$CellContext`colorList, Span[5, 8]], 4]}]], " fp_gen ", Dynamic[ SetterBar[ Dynamic[$CellContext`fpG$$], Range[4] - 1]], " fp_flip ", Checkbox[ Dynamic[$CellContext`flip$$]]}], Row[{"IJKL Style ", Checkbox[ Dynamic[$CellContext`IJKLstyle$$]], Spacer[5], " n1 ", Dynamic[ SetterBar[ Dynamic[$CellContext`n1$$], Map[# -> Part[$CellContext`octImag$$, #]& , Range[7]]]], " n2 ", Dynamic[ SetterBar[ Dynamic[$CellContext`n2$$], Map[# -> Part[$CellContext`octImag$$, #]& , Range[7]]]], " n3 ", Dynamic[ SetterBar[ Dynamic[$CellContext`n3$$], Map[# -> Part[$CellContext`octImag$$, #]& , Range[7]]]]}]}], "2) Math: Geometry: Dynkin Diagram Algebra Creator" -> Column[{ Row[{ Button[" reset ", $CellContext`init$$ = True], Spacer[25], "menu of Dynkin diagrams: ", PopupMenu[ Dynamic[$CellContext`selAlgebra$$], { "A1", "A2", "A3", "A4", "A5", "A6", "A7", "B2", "B3", "B4", "B5", "B6", "B7", "B8", "C3", "C4", "C5", "C6", "C7", "C8", "D4", "D5", "D6", "D7", "D8", "E6", "E7", "E8", "F4", "G2", "H3", "H4", "CUBE2", "CUBE3", "CUBE4", "CUBE5", "CUBE6", "CUBE7", "FINITE1", "FOLDED1", "FOLDED2", "EXTENDED1", "LOOPED1", "MONSTER1", "MONSTER2"}], Spacer[25], "recognize as type: ", Dynamic[ SetterBar[ Dynamic[$CellContext`affineTrk$$], { 0 -> "finite", 1 -> "affine", 2 -> "hyperbolic", 3 -> "very extended"}]]}], Row[{"Coxeter geometric permutation: ", Dynamic[ Slider[ Dynamic[$CellContext`selDynkin$$], { 1, 2^Min[8, $CellContext`rank$$], 1}, ImageSize -> 225, ContinuousAction -> False]], Dynamic[$CellContext`selDynkin$$], Spacer[10], "name: ", Dynamic[$CellContext`permName$$]}]}], "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer" -> Column[{ Row[{"projection ", PopupMenu[ Dynamic[$CellContext`selCoxeter$$], { "D+1=BC2", "D+1=BC3", "D+1=BC4", "D+1=BC5", "D+1=BC6", "D+1=BC7", "D+1=BC8", "A5(6)", "A7(8)", "E6(12)", "E7(18)", "20", "24", "E8(30)", "Pascal2", "Pascal3", "Pascal4", "Pascal5", "Pascal6", "Pascal7"}], " menu 1 ", PopupMenu[ Dynamic[$CellContext`bAND1Name$$], { "E8", "E8 hexes", "E8 hyper", "E8 3", "E8 3D", "E8 24x10", "E8 12x5", "E8 Petrie", "E8 in E6", "E7", "E6", "E6 a", "E5", "E4", "F4", "H4", "G2", "Tesseract", "16 cell", "24 cell", "24 cell D4", "24 cell G2", "600 cell 3D", "Hydrogen", "none"}], " 2 ", PopupMenu[ Dynamic[$CellContext`bAND2Name$$], { "F4 tris", "F4 to G2", "F4 star", "2 cube Pascal", "3 cube Pascal", "4 cube Pascal", "5 cube Pascal", "6 cube Pascal", "7 cube Pascal", "8 cube Pascal", "2 cube Petrie", "3 cube Petrie", "4 cube Petrie", "5 cube Petrie", "6 cube Petrie", "7 cube Petrie", "8 cube Petrie", "lepton info", "quark info", "quark column", "binary", "binary star", "binary square", "devolution"}], " vertices=", Dynamic[ Length[$CellContext`fltrdSubPlot$$]], " edges=", Dynamic[ Length[$CellContext`elines$$]], " trialities=", Dynamic[ Length[$CellContext`tlines$$]], " clicked edges=", Dynamic[ Length[ If[$CellContext`physics$$, $CellContext`plines$$, \ $CellContext`vlines$$]]]}], Row[{"axes ", Checkbox[ Dynamic[$CellContext`showAxes$$]], " edges ", Checkbox[ Dynamic[$CellContext`showEdges$$]], " physics ", Checkbox[ Dynamic[$CellContext`physics$$]], " labels ", Checkbox[ Dynamic[$CellContext`showPtext$$]], " axes locators ", Checkbox[ Dynamic[$CellContext`useDimLocs$$]], " ", RadioButtonBar[ Dynamic[$CellContext`p3D$$], {" 2D", " 3D"}], " triality ", TogglerBar[ Dynamic[$CellContext`tT$$], { "T1", "T1p", "T2", "T2p", "T4", "T4p"}], "", " steps ", Slider[ Dynamic[$CellContext`steps$$], {1, 60, 1}, ImageSize -> 60, ContinuousAction -> False], Dynamic[$CellContext`steps$$]}]}], "4) Physics: Particle: Fundamental Quantum Element Builder" -> Grid[{{" anti", "pType", "spin", "color", "gen", "row"}, { Checkbox[ Dynamic[$CellContext`anti$$]], RadioButtonBar[ Dynamic[$CellContext`ptype$$], {1, 2}], Dynamic[ SetterBar[ Dynamic[$CellContext`s0$$], $CellContext`spList, Enabled -> If[$CellContext`r1$$ == 3, False, True]]], Dynamic[ SetterBar[ Dynamic[$CellContext`c0$$], Part[$CellContext`colorList, Span[5, 8]], Enabled -> If[ Or[$CellContext`r1$$ == 1, $CellContext`r1$$ == 5], False, True]]], Dynamic[ SetterBar[ Dynamic[$CellContext`g0$$], Range[3], Enabled -> If[$CellContext`r1$$ > 2, False, True]]], Dynamic[ PopupMenu[ Dynamic[$CellContext`r0$$], $CellContext`flavorRows]]}}], "5) Physics: Nuclear: Meson Particle Selector" -> Grid[{{"quark", SetterBar[ Dynamic[$CellContext`c2a$$], {"r", "g", "b"}], SetterBar[ Dynamic[$CellContext`s2$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}], RadioButtonBar[ Dynamic[$CellContext`q2a$$], { "UpQuark" -> "u", "DownQuark" -> "d", "StrangeQuark" -> "s", "CharmQuark" -> "c", "BottomQuark" -> "b", "TopQuark" -> "t"}]}, {"antiquark", SetterBar[ Dynamic[$CellContext`c2a$$], {"r", "g", "b"}], SetterBar[ Dynamic[$CellContext`s3$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}], RadioButtonBar[ Dynamic[$CellContext`q2b$$], { "UpQuarkBar" -> "\!\(\*OverscriptBox[\(u\), \(_\)]\)", "DownQuarkBar" -> "\!\(\*OverscriptBox[\(d\), \(_\)]\)", "StrangeQuarkBar" -> "\!\(\*OverscriptBox[\(s\), \(_\)]\)", "CharmQuarkBar" -> "\!\(\*OverscriptBox[\(c\), \(_\)]\)", "BottomQuarkBar" -> "\!\(\*OverscriptBox[\(b\), \(_\)]\)", "TopQuarkBar" -> "\!\(\*OverscriptBox[\(t\), \(_\)]\)"}]}}], "6) Physics: Atomic: Baryon Particle Selector" -> Column[{ Row[{"r ", Item[ SetterBar[ Dynamic[$CellContext`s4$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}]], RadioButtonBar[ Dynamic[$CellContext`q3a$$], { "UpQuark" -> "u", "DownQuark" -> "d", "StrangeQuark" -> "s", "CharmQuark" -> "c", "BottomQuark" -> "b", "TopQuark" -> "t"}], Spacer[20], " g", SetterBar[ Dynamic[$CellContext`s5$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}], RadioButtonBar[ Dynamic[$CellContext`q3b$$], { "UpQuark" -> "u", "DownQuark" -> "d", "StrangeQuark" -> "s", "CharmQuark" -> "c", "BottomQuark" -> "b", "TopQuark" -> "t"}]}], Row[{"b ", SetterBar[ Dynamic[$CellContext`s6$$], { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}], RadioButtonBar[ Dynamic[$CellContext`q3c$$], { "UpQuark" -> "u", "DownQuark" -> "d", "StrangeQuark" -> "s", "CharmQuark" -> "c", "BottomQuark" -> "b", "TopQuark" -> "t"}]}]}], "7) Chemistry: Periodic Table Element Selector" -> Column[{ Row[{"isotope ", SetterBar[ Dynamic[$CellContext`isotope$$], {-3, -2, -1, 0, 1, 2, 3}], " tooltip element display ", PopupMenu[ Dynamic[$CellContext`ttED$$], { "Abbreviation", "AbsoluteBoilingPoint", "AbsoluteMeltingPoint", "AdiabaticIndex", "AllotropeNames", "AllotropicMultiplicities", "AlternateNames", "AlternateStandardNames", "AtomicNumber", "AtomicRadius", "AtomicWeight", "Block", "BoilingPoint", "BrinellHardness", "BulkModulus", "CASNumber", "Color", "CommonCompoundNames", "CovalentRadius", "CriticalPressure", "CriticalTemperature", "CrustAbundance", "CrystalStructure", "CuriePoint", "DecayMode", "Density", "DiscoveryCountries", "DiscoveryYear", "ElectricalConductivity", "ElectricalType", "ElectronAffinity", "ElectronConfiguration", "ElectronConfigurationString", "Electronegativity", "ElectronShellConfiguration", "FusionHeat", "GasAtomicMultiplicities", "Group", "HalfLife", "HumanAbundance", "IconColor", "IonizationEnergies", "IsotopeAbundances", "KnownIsotopes", "LatticeAngles", "LatticeConstants", "Lifetime", "LiquidDensity", "MagneticType", "MassMagneticSusceptibility", "MeltingPoint", "Memberships", "MeteoriteAbundance", "MohsHardness", "MolarMagneticSusceptibility", "MolarVolume", "Name", "NeelPoint", "NeutronCrossSection", "NeutronMassAbsorption", "OceanAbundance", "Period", "Phase", "PoissonRatio", "QuantumNumbers", "Radioactive", "RefractiveIndex", "Resistivity", "ShearModulus", "SolarAbundance", "SoundSpeed", "SpaceGroupName", "SpaceGroupNumber", "SpecificHeat", "StableIsotopes", "StandardName", "SuperconductingPoint", "ThermalConductivity", "ThermalExpansion", "UniverseAbundance", "Valence", "VanDerWaalsRadius", "VaporizationHeat", "VickersHardness", "VolumeMagneticSusceptibility", "YoungModulus"}]}], Row[{" n ", SetterBar[ Dynamic[$CellContext`n0$$], {1, 2, 3, 4, 5, 6, 7, 8}], " 3D ", Checkbox[ Dynamic[$CellContext`view3D$$], {False, True}], " explode view ", Slider[ Dynamic[$CellContext`explode$$], {1, 8, 1}, Enabled -> If[ Dynamic[$CellContext`view3D$$], True, False]], " electron density ", Checkbox[ Dynamic[$CellContext`density$$], {False, True}], " ", RadioButtonBar[ Dynamic[$CellContext`stowe$$], { True -> "Stowe", False -> "Scerri"}, Enabled -> If[ Dynamic[$CellContext`view3D$$], True, False]]}]}], "8) Biology: Life: nD Human Machine Interface" -> Column[{ Row[{" art print ", Checkbox[ Dynamic[$CellContext`artPrint$$]], " data set ", Dynamic[ PopupMenu[ Dynamic[$CellContext`dsName$$], $CellContext`dsNames]], Dynamic[$CellContext`ds$$ = \ $CellContext`position[$CellContext`dsNames, $CellContext`dsName$$]]}], Row[{"limit ", Checkbox[ Dynamic[$CellContext`limitToRange$$]], " pSize ", PopupMenu[ Dynamic[$CellContext`pSize$$], {$CellContext`tiny, \ $CellContext`small, $CellContext`nrml, $CellContext`big, $CellContext`huge}], " \!\(\*SuperscriptBox[\(10\), \(n\)]\) zoom ", Dynamic[ Slider[ Dynamic[$CellContext`zoom$$], {-24, 25, 0.5}, ImageSize -> 100]], Dynamic[$CellContext`zoom$$], " particle scale ", Dynamic[ Slider[ Dynamic[$CellContext`scale$$], {0, 1, 1/50.}, ImageSize -> 50]], Dynamic[ NumberForm[ Subscript[$CellContext`scale$$, $CellContext`scaled], 4]], " ticks ", Dynamic[ Slider[ Dynamic[$CellContext`tickNum$$], {0, 50, 1}, ImageSize -> 50]], Dynamic[$CellContext`tickNum$$], " frame ", Dynamic[ Slider[ Dynamic[$CellContext`range$$], {0, 2, 0.01}, ImageSize -> 50]], Dynamic[ NumberForm[ Subscript[$CellContext`range$$, $CellContext`scaled], 4]]}]}]}, Dynamic[$CellContext`interactionPane$$]]], \ {{$CellContext`IJKLstyle$$, False}, 0, ControlType -> None}, {{$CellContext`octImag$$, { Subscript[$CellContext`\[ScriptE], 1], Subscript[$CellContext`\[ScriptE], 2], Subscript[$CellContext`\[ScriptE], 3], Subscript[$CellContext`\[ScriptE], 4], Subscript[$CellContext`\[ScriptE], 5], Subscript[$CellContext`\[ScriptE], 6], Subscript[$CellContext`\[ScriptE], 7]}}, 0, ControlType -> None}, {{$CellContext`sm$$, 4}, 0, ControlType -> None}, {{$CellContext`fpC$$, 1}, 0, ControlType -> None}, {{$CellContext`fpG$$, 1}, 0, ControlType -> None}, {{$CellContext`altMask$$, False}, 0, ControlType -> None}, {{$CellContext`invMask$$, True}, 0, ControlType -> None}, {{$CellContext`flip$$, True}, 0, ControlType -> None}, {{$CellContext`n1$$, 1}, 0, ControlType -> None}, {{$CellContext`n2$$, 2}, 0, ControlType -> None}, {{$CellContext`n3$$, 3}, 0, ControlType -> None}, {{$CellContext`fPi$$, 1}, 0, ControlType -> None}, {$CellContext`selAlgebra$$, "A1", ControlType -> None}, {$CellContext`selDynkin$$, 1, ControlType -> None}, {$CellContext`dynkTbl$$, {{{{{1, 2}, 1}}, {}, 0}}, ControlType -> None}, {$CellContext`ptsLoc$$, {{{1, 2}, 1}}, ControlType -> None}, {$CellContext`dynkin$$, {}, ControlType -> None}, {$CellContext`affine$$, 0, ControlType -> None}, {$CellContext`rank$$, 1, ControlType -> None}, {$CellContext`alg1$$, "A", ControlType -> None}, {$CellContext`alg$$, "A1", ControlType -> None}, {$CellContext`group$$, "Sl(2)", ControlType -> None}, {$CellContext`permName$$, "Parent", ControlType -> None}, {$CellContext`init$$, True, ControlType -> None}, {$CellContext`ptDD$$, {0, 0}, ControlType -> None}, {$CellContext`algTrk$$, "A1", ControlType -> None}, {$CellContext`permTrk$$, {0, 0}, ControlType -> None}, {$CellContext`ptDDTrk$$, {0, 0}, ControlType -> None}, {$CellContext`selAlgebraTrk$$, "A1", ControlType -> None}, {$CellContext`selDynkinTrk$$, 1, ControlType -> None}, {$CellContext`affineTrk$$, 0, ControlType -> None}, {$CellContext`ptsLocSav$$, 0, ControlType -> None}, {$CellContext`dynkSav$$, 0, ControlType -> None}, {{$CellContext`fileOnly$$, False}, 0, ControlType -> None}, {{$CellContext`artPrint$$, False}, 0, ControlType -> None}, {{$CellContext`scale$$, 0.54}, 0, ControlType -> None}, {{$CellContext`cylR$$, 0.026}, 0, ControlType -> None}, {{$CellContext`tickNum$$, 4}, 0, ControlType -> None}, {{$CellContext`range$$, 1.5}, 0, ControlType -> None}, {{$CellContext`limitToRange$$, True}, 0, ControlType -> None}, {{$CellContext`pt$$, {0, 0, 0}}, 0, ControlType -> None}, {{$CellContext`zoom$$, 0}, 0, ControlType -> None}, {{$CellContext`favorite$$, 3}, 0, ControlType -> None}, {{$CellContext`pGrad$$, 0}, 0, ControlType -> None}, {{$CellContext`face$$, 1}, 0, ControlType -> None}, {{$CellContext`auxData$$, False}, 0, ControlType -> None}, {{$CellContext`showAxes$$, False}, 0, ControlType -> None}, {{$CellContext`showPartVert$$, True}, 0, ControlType -> None}, {{$CellContext`showEdges$$, True}, 0, ControlType -> None}, {{$CellContext`showSurfaces$$, False}, 0, ControlType -> None}, {{$CellContext`showPolySurfaces$$, True}, 0, ControlType -> None}, {{$CellContext`showPvecs$$, False}, 0, ControlType -> None}, {{$CellContext`showPtext$$, True}, 0, ControlType -> None}, {{$CellContext`showPlocs$$, False}, 0, ControlType -> None}, {{$CellContext`showPmass$$, False}, 0, ControlType -> None}, {{$CellContext`showPerim$$, False}, 0, ControlType -> None}, {{$CellContext`eGrad$$, 44}, 0, ControlType -> None}, {{$CellContext`edgeVals$$, {{"All", 6}}}, 0, ControlType -> None}, {{$CellContext`anim8EdgeList$$, False}, 0, ControlType -> None}, {{$CellContext`eColorPos$$, True}, 0, ControlType -> None}, {{$CellContext`eSteps$$, 1}, 0, ControlType -> None}, {{$CellContext`eWnd$$, 100}, 0, ControlType -> None}, {{$CellContext`innerMag$$, 0}, 0, ControlType -> None}, {{$CellContext`dimTrim$$, 8}, 0, ControlType -> None}, {{$CellContext`XY$$, {20, 20, 20}}, 0, ControlType -> None}, {{$CellContext`tT$$, {}}, 0, ControlType -> None}, {{$CellContext`showClr$$, False}, 0, ControlType -> None}, {{$CellContext`showClickVerts$$, False}, 0, ControlType -> None}, {{$CellContext`vOverlapColor$$, False}, 0, ControlType -> None}, {{$CellContext`ltps$$, {}}, 0, ControlType -> None}, {{$CellContext`physics$$, True}, 0, ControlType -> None}, {{$CellContext`useDimLocs$$, False}, 0, ControlType -> None}, {{$CellContext`dlXs$$, $CellContext`dls[{1}]}, 0, ControlType -> None}, {{$CellContext`dlYs$$, $CellContext`dls[{2}]}, 0, ControlType -> None}, {{$CellContext`dlZs$$, $CellContext`dls[{3}]}, 0, ControlType -> None}, {{$CellContext`xy$$, {1, 1}}, 0, ControlType -> None}, {{$CellContext`zz$$, 1}, 0, ControlType -> None}, {{$CellContext`xyVwPnt$$, {0.75, 0.75}}, 0, ControlType -> None}, {{$CellContext`zVwPnt$$, 0.75}, 0, ControlType -> None}, {{$CellContext`steps$$, 5}, 0, ControlType -> None}, {{$CellContext`nDcamera$$, 1.}, 0, ControlType -> None}, {{$CellContext`perspective$$, False}, 0, ControlType -> None}, {{$CellContext`pthRot$$, "Trans"}, 0, ControlType -> None}, {{$CellContext`pthPtCds$$, "Identity"}, 0, ControlType -> None}, {{$CellContext`ds$$, 3}, 0, ControlType -> None}, {{$CellContext`pSize$$, $CellContext`nrml}, 0, ControlType -> None}, {{$CellContext`pListName$$, "None"}, 0, ControlType -> None}, {{$CellContext`dsName$$, "physics"}, 0, ControlType -> None}, {{$CellContext`p3D$$, " 2D"}, 0, ControlType -> None}, {{$CellContext`infile$$, "./auxData.m"}, 0, ControlType -> None}, {{$CellContext`auxFile$$, "./auxData.xls"}, 0, ControlType -> None}, {{$CellContext`fileOut$$, False}, 0, ControlType -> None}, {{$CellContext`outFileDir$$, "./"}, 0, ControlType -> None}, {{$CellContext`outFile$$, "E8out"}, 0, ControlType -> None}, {{$CellContext`outFileType$$, ".png"}, 0, ControlType -> None}, {{$CellContext`H$$, {0, 0, 0, 0, 0, 0, 0, 0}}, 0, ControlType -> None}, {{$CellContext`V$$, {0, 0, 0, 0, 0, 0, 0, 0}}, 0, ControlType -> None}, {{$CellContext`Z$$, {0, 0, 0, 0, 0, 0, 0, 0}}, 0, ControlType -> None}, {{$CellContext`selCoxeter$$, ""}, 0, ControlType -> None}, {{$CellContext`bAND$$, 1}, 0, ControlType -> None}, {{$CellContext`bAND1Name$$, "Hydrogen"}, 0, ControlType -> None}, {{$CellContext`bAND2Name$$, ""}, 0, ControlType -> None}, {{$CellContext`fltrdSubPlot$$, CompressedData[" 1:eJwd0wOfEAYAxuEue7Va1lXbsm1zC5ddl3XZ5rK11dJybbll27Zt20+9v//z Ed7A4DZBIQGhLOB7oUIThrCEIzwRiEgkIhOFqEQjOj8Qg5j8SCxi8xNxiEs8 4pOAhCQiMUlISjICSU4KUvIzv/ArqUhNGtKSjvRkICOZyEwWspKN7OQgJ7nI TR7yko/8FKAghShMEYpSjOKUoCSlKE0ZyvIbv1OO8lSgIkFUojJVqEo1qlOD mtSiNnWoSz3q04BgGtKIxjShKc1oTgta0orWhNCGtrSjPR3oSCc604WudKM7 PehJL3rTh770oz8DGMggBvMHQxjKMIYzgpGMYjRjGMs4xjOBiUxiMlP4k7+Y yjT+ZjozmMksZvMPc5jLPOazgIUsYjFL+Jf/WMoylrOClaxiNWv4n7WsYz0b 2MgmNrOFrWxjOzvYyS52s4e97GM/BzjIIQ5zhKMc4zgnOMkpTnOGs5zjPBe4 yCUuc4WrXOM6N7jJLW5zh7vc4z4PeMgjHvOEpzzjOS94ySte84a3vOM9H/jI Jz7zhW/n/wqYtIE2 "]}, 0, ControlType -> None}, {{$CellContext`fullVerts$$, {}}, 0, ControlType -> None}, {{$CellContext`verts$$, {}}, 0, ControlType -> None}, {{$CellContext`rectification$$, 0}, 0, 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True}, 0, ControlType -> None}, {{$CellContext`anti$$, False}, 0, ControlType -> None}, {{$CellContext`ptype$$, 2}, 0, ControlType -> None}, {{$CellContext`r1$$, 1}, 0, ControlType -> None}, {{$CellContext`c0$$, "w"}, 0, ControlType -> None}, {{$CellContext`s0$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`s1$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`g0$$, 1}, 0, ControlType -> None}, {{$CellContext`r0$$, "l"}, 0, ControlType -> None}, {{$CellContext`q2a$$, "UpQuark"}, 0, ControlType -> None}, {{$CellContext`s2$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`c2a$$, "r"}, 0, ControlType -> None}, {{$CellContext`q2b$$, "DownQuarkBar"}, 0, ControlType -> None}, {{$CellContext`s3$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`q3a$$, "UpQuark"}, 0, ControlType -> None}, {{$CellContext`s4$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`q3b$$, "UpQuark"}, 0, ControlType -> None}, {{$CellContext`s5$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`q3c$$, "UpQuark"}, 0, ControlType -> None}, {{$CellContext`s6$$, Overscript["L", "\[Vee]"]}, 0, ControlType -> None}, {{$CellContext`isotope$$, 0}, 0, ControlType -> None}, {{$CellContext`ttED$$, "ElectronConfigurationString"}, 0, ControlType -> None}, {{$CellContext`n0$$, 8}, 0, ControlType -> None}, {{$CellContext`view3D$$, True}, 0, ControlType -> None}, {{$CellContext`density$$, False}, 0, ControlType -> None}, {{$CellContext`explode$$, 4}, 0, ControlType -> None}, {{$CellContext`stowe$$, False}, 0, ControlType -> None}}, "Options" :> { ContentSize -> {750., 500.}, LocalizeVariables -> True, PreserveImageOptions -> True, SynchronousUpdating -> False, SynchronousInitialization -> False, TrackedSymbols :> {$CellContext`interactionPane$$, \ $CellContext`IJKLstyle$$, $CellContext`fpC$$, $CellContext`fpG$$, \ $CellContext`flip$$, $CellContext`sm$$, $CellContext`altMask$$, \ $CellContext`invMask$$, $CellContext`n1$$, $CellContext`n2$$, \ $CellContext`n3$$, $CellContext`init$$, $CellContext`selAlgebra$$, \ $CellContext`selDynkin$$, $CellContext`affineTrk$$, $CellContext`ptDD$$, \ $CellContext`refresh$$, $CellContext`selCoxeter$$, $CellContext`bAND1Name$$, \ $CellContext`bAND2Name$$, $CellContext`locPtCdArr$$, \ $CellContext`showPtext$$, $CellContext`pthRot$$, $CellContext`showAxes$$, \ $CellContext`steps$$, $CellContext`p3D$$, $CellContext`showEdges$$, \ $CellContext`physics$$, $CellContext`useDimLocs$$, $CellContext`tT$$, \ $CellContext`anti$$, $CellContext`ptype$$, $CellContext`c0$$, \ $CellContext`s0$$, $CellContext`s0$$, $CellContext`g0$$, $CellContext`r0$$, \ $CellContext`q2a$$, $CellContext`s2$$, $CellContext`c2a$$, \ $CellContext`q2b$$, $CellContext`s3$$, $CellContext`q3a$$, $CellContext`s4$$, \ $CellContext`q3b$$, $CellContext`s5$$, $CellContext`q3c$$, $CellContext`s6$$, \ $CellContext`n0$$, $CellContext`view3D$$, $CellContext`density$$, \ $CellContext`explode$$, $CellContext`ttED$$, $CellContext`isotope$$, \ $CellContext`stowe$$, $CellContext`bAND$$}}, "DefaultOptions" :> {}], ImageSizeCache -> {768., {307., 312.}}, SingleEvaluation -> True], Deinitialization :> None, DynamicModuleValues :> {}, Initialization :> ({$CellContext`pdList = { "1) Math: Numbers: Octonion Fano Plane & Cubic", "2) Math: Geometry: Dynkin Diagram Algebra Creator", "3) Math: Algebra: E8 Lie Algebra & Subgroups Visualizer", "4) Physics: Particle: Fundamental Quantum Element Builder", "5) Physics: Nuclear: Meson Particle Selector", "6) Physics: Atomic: Baryon Particle Selector", "7) Chemistry: Periodic Table Element Selector", "8) Biology: Life: nD Human Machine Interface"}, \ $CellContext`doFano := With[{$CellContext`local$ = $CellContext`localFano}, Module[$CellContext`local$, $CellContext`d8Q := \ $CellContext`invMask$$ != $CellContext`altMask$$; $CellContext`doD8 := Or[ And[$CellContext`flip$$, $CellContext`d8Q], And[ Not[$CellContext`flip$$], Not[$CellContext`d8Q]]]; $CellContext`excFanoQ := And[$CellContext`fpC$$ == 0, $CellContext`fpG$$ == 0]; $CellContext`fPi$$ := Part[ If[$CellContext`doD8, $CellContext`fpD8, $CellContext`fpC8], If[$CellContext`excFanoQ, 1, 0] + 2^2 $CellContext`fB[$CellContext`fpC$$, 2] + 2^2 $CellContext`fB[$CellContext`fpC$$, 1] + $CellContext`fB[$CellContext`fpG$$, 2] + $CellContext`fB[$CellContext`fpG$$, 1]]; $CellContext`oct2p := \ $CellContext`spConv[$CellContext`invMask$$, Part[$CellContext`flavorListStr, If[$CellContext`excFanoQ, 5, If[$CellContext`fpG$$ == 0, If[$CellContext`sm$$ == 1, 3, 4], If[$CellContext`fpC$$ == 0, 1, 2]]], If[$CellContext`altMask$$, 2, 1], If[$CellContext`excFanoQ, 1, If[$CellContext`fpG$$ == 0, $CellContext`fpC$$, $CellContext`fpG$$]]], If[$CellContext`excFanoQ, "\" \"", Part[ Part[$CellContext`colorList, Span[5, 8]], 1 + $CellContext`fpC$$]], Part[$CellContext`spList, $CellContext`sm$$]]; $CellContext`fM[ Pattern[$CellContext`perm, Blank[]], Pattern[$CellContext`triads, Blank[]], Pattern[$CellContext`sign, Blank[]]] := ($CellContext`fanoMult[$CellContext`perm, \ $CellContext`triads, $CellContext`sign]; $CellContext`fm = Table[ If[$CellContext`i == $CellContext`j, If[$CellContext`i == 8, 1, -1], Part[$CellContext`fSign, $CellContext`i, $CellContext`j] Part[$CellContext`fMult, $CellContext`i, $CellContext`j]], \ {$CellContext`i, 8}, {$CellContext`j, 8}]; $CellContext`fm = Transpose[ Join[{ RotateRight[ Part[$CellContext`fm, 8]]}, Table[ RotateRight[ Part[$CellContext`fm, $CellContext`i]], {$CellContext`i, 7}]]]); $CellContext`fM[ Pattern[$CellContext`perm, Blank[]], Pattern[$CellContext`triads, Blank[]]] := $CellContext`fM[$CellContext`perm, \ $CellContext`triads, 0]; $CellContext`fM[ Pattern[$CellContext`triads, Blank[]]] := $CellContext`fM[ Range[7], $CellContext`triads, 0]; {$CellContext`triads, $CellContext`flatFanoStyled, \ $CellContext`flatFano, $CellContext`firstFlipSign} = \ $CellContext`getTriads[$CellContext`invMask$$, $CellContext`altMask$$, \ $CellContext`fPi$$, $CellContext`sm$$]; $CellContext`fM[$CellContext`triads]; If[ Or[$CellContext`localize, $CellContext`refresh$$], $CellContext`addParticles[{$CellContext`oct2p}]]; \ $CellContext`chkOctStyle := If[$CellContext`IJKLstyle$$, Unset[$CellContext`\[DoubleStruckJ]]; Unset[$CellContext`J]; Unset[$CellContext`\[DoubleStruckK]]; Unset[K]; Unset[$CellContext`\[DoubleStruckL]]; Unset[$CellContext`L], $CellContext`\[DoubleStruckJ] = \ ($CellContext`J = Subscript[$CellContext`\[ScriptE], 2]); $CellContext`\[DoubleStruckK] = (K = Subscript[$CellContext`\[ScriptE], 3]); $CellContext`\[DoubleStruckL] = Subscript[$CellContext`\[ScriptE], 4]; Null]; $CellContext`chkOctStyle; $CellContext`octImag$$ := Most[ If[$CellContext`IJKLstyle$$, $CellContext`octIJKL, \ $CellContext`oct]]; $CellContext`octPM := If[$CellContext`IJKLstyle$$, $CellContext`pmOctIJKL, \ $CellContext`pmOct]; $CellContext`pmChk[ Pattern[$CellContext`p, Blank[]]] := If[ MemberQ[$CellContext`pmOct, $CellContext`p], \ $CellContext`pmOct, $CellContext`pmOctIJKL]; $CellContext`posChk[ Pattern[$CellContext`p, Blank[]]] := $CellContext`position[ $CellContext`pmChk[$CellContext`p], $CellContext`p]; \ $CellContext`fanoChk[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`octPM, $CellContext`posChk[$CellContext`p]]; $CellContext`fmTable[ Pattern[$CellContext`f, Blank[]]] := Table[ Style[ ReleaseHold[$CellContext`f], If[ Or[$CellContext`i == 1, $CellContext`j == 1, $CellContext`i == $CellContext`j], Red, Black]], {$CellContext`i, 8}, {$CellContext`j, 8}]; $CellContext`fmDispN := MatrixForm[ ReplacePart[ $CellContext`fmTable[ Hold[ Part[$CellContext`fm, $CellContext`i, $CellContext`j]]], {1, 1} -> "\!\(\*\nStyleBox[\"0\",\nFontColor->RGBColor[1, 0, \ 0]]\)\!\(\*\nStyleBox[\"\[RightTeeArrow]\",\nFontColor->RGBColor[1, 0, \ 0]]\)\!\(\*\nStyleBox[\"1\",\nFontColor->RGBColor[1, 0, 0]]\)"]]; \ $CellContext`fmDisp\[ScriptE] := MatrixForm[ $CellContext`fmTable[ Hold[ $CellContext`fanoChk[ SmallCircle[ Subscript[$CellContext`\[ScriptE], $CellContext`i - 1], Subscript[$CellContext`\[ScriptE], $CellContext`j - 1]]]]]]; $CellContext`basis[ Pattern[$CellContext`p, Blank[]]] := $CellContext`position[$CellContext`flatFano, \ $CellContext`p]; $CellContext`basis[ Pattern[$CellContext`in, Blank[List]]] := Map[$CellContext`basis, $CellContext`in]; $CellContext`basisRev[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`flatFano, $CellContext`p]; \ $CellContext`basisRev[ Pattern[$CellContext`in, Blank[List]]] := Map[$CellContext`basisRev, $CellContext`in]; SmallCircle[ Subscript[$CellContext`\[ScriptE], 0], Subscript[$CellContext`\[ScriptE], 0]] := 1; SmallCircle[ Pattern[$CellContext`a, Blank[]], Subscript[$CellContext`\[ScriptE], 0]] := $CellContext`a; SmallCircle[ Subscript[$CellContext`\[ScriptE], 0], Pattern[$CellContext`b, Blank[]]] := $CellContext`b; SmallCircle[ Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`i, Blank[Integer]]], Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`i, Blank[Integer]]]] := -1; SmallCircle[ PatternTest[ Pattern[$CellContext`a, Blank[]], NumericQ], PatternTest[ Pattern[$CellContext`b, Blank[]], NumericQ]] := $CellContext`a $CellContext`b; SmallCircle[ PatternTest[ Pattern[$CellContext`a, Blank[]], NumericQ], Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`b, Blank[]]]] := $CellContext`a Subscript[$CellContext`\[ScriptE], $CellContext`b]; SmallCircle[ Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`a, Blank[]]], PatternTest[ Pattern[$CellContext`b, Blank[]], NumericQ]] := $CellContext`b Subscript[$CellContext`\[ScriptE], $CellContext`a]; SmallCircle[PatternTest[ Pattern[$CellContext`a, Blank[]], NumericQ] Pattern[$CellContext`b, Blank[]], Pattern[$CellContext`c, Blank[]]] := $CellContext`a SmallCircle[$CellContext`b, $CellContext`c]; SmallCircle[ Pattern[$CellContext`a, Blank[]], PatternTest[ Pattern[$CellContext`b, Blank[]], NumericQ] Pattern[$CellContext`c, Blank[]]] := $CellContext`b SmallCircle[$CellContext`a, $CellContext`c]; SmallCircle[ Pattern[$CellContext`a, Blank[List]], Pattern[$CellContext`b, Blank[]]] := Map[SmallCircle[#, $CellContext`b]& , $CellContext`a]; SmallCircle[ Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[List]]] := Map[SmallCircle[$CellContext`a, #]& , $CellContext`b]; Pattern[$CellContext`ep, SmallCircle[ Pattern[$CellContext`a, Blank[Plus]], Pattern[$CellContext`b, Blank[]]]] := Block[{SmallCircle}, Distribute[$CellContext`ep]]; Pattern[$CellContext`ep, SmallCircle[ Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[Plus]]]] := Block[{SmallCircle}, Distribute[$CellContext`ep]]; SmallCircle[ Pattern[$CellContext`a, Blank[Times]], Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`b, Blank[]]]] := Select[$CellContext`a, NumericQ] SmallCircle[ Select[$CellContext`a, Not[ NumericQ[#]]& ], Subscript[$CellContext`\[ScriptE], $CellContext`b]]; SmallCircle[ Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`a, Blank[]]], Pattern[$CellContext`b, Blank[Times]]] := Select[$CellContext`b, NumericQ] SmallCircle[ Subscript[$CellContext`\[ScriptE], $CellContext`a], Select[$CellContext`b, Not[ NumericQ[#]]& ]]; Condition[ SmallCircle[ Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`i, Blank[Integer]]], Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`j, Blank[Integer]]]], $CellContext`i != $CellContext`j] := Sign[ Part[$CellContext`fm, 1 + Mod[$CellContext`i, 8], 1 + Mod[$CellContext`j, 8]]] Subscript[$CellContext`\[ScriptE], Abs[ Part[$CellContext`fm, 1 + Mod[$CellContext`i, 8], 1 + Mod[$CellContext`j, 8]]]]; $CellContext`associator[ Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`a, Blank[]]], Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`b, Blank[]]], Subscript[$CellContext`\[ScriptE], Pattern[$CellContext`c, Blank[]]]] := Expand[SmallCircle[ SmallCircle[ Subscript[$CellContext`\[ScriptE], $CellContext`a], Subscript[$CellContext`\[ScriptE], $CellContext`b]], Subscript[$CellContext`\[ScriptE], $CellContext`c]] - SmallCircle[ Subscript[$CellContext`\[ScriptE], $CellContext`a], SmallCircle[ Subscript[$CellContext`\[ScriptE], $CellContext`b], Subscript[$CellContext`\[ScriptE], $CellContext`c]]]]; \ $CellContext`associator[ Pattern[$CellContext`a, Blank[Integer]], Pattern[$CellContext`b, Blank[Integer]], Pattern[$CellContext`c, Blank[Integer]]] := $CellContext`associator[ Subscript[$CellContext`\[ScriptE], $CellContext`a], Subscript[$CellContext`\[ScriptE], $CellContext`b], Subscript[$CellContext`\[ScriptE], $CellContext`c]]; \ $CellContext`octonion[ Pattern[$CellContext`p$, Blank[]]] := Total[$CellContext`p$ Join[{1}, $CellContext`octImag$$]]; $CellContext`commutator[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Simplify[ Chop[ SmallCircle[$CellContext`x, $CellContext`y] - SmallCircle[$CellContext`y, $CellContext`x]]]; \ $CellContext`derivation[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]][ Pattern[$CellContext`a, Blank[]]] := $CellContext`commutator[ $CellContext`commutator[$CellContext`x, $CellContext`y], \ $CellContext`a] - 3 (SmallCircle[ SmallCircle[$CellContext`x, $CellContext`y], $CellContext`a] - SmallCircle[$CellContext`x, SmallCircle[$CellContext`y, $CellContext`a]]); \ $CellContext`derMatrix[ Pattern[$CellContext`x$, Blank[]], Pattern[$CellContext`y$, Blank[]]] := Table[ Coefficient[ $CellContext`derivation[$CellContext`x$, $CellContext`y$][ Part[$CellContext`octImag$$, $CellContext`i]], Part[$CellContext`octImag$$, $CellContext`j]], \ {$CellContext`j, 1, 7}, {$CellContext`i, 1, 7}]; $CellContext`derVector[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Flatten[ $CellContext`derMatrix[$CellContext`x, $CellContext`y]]; \ $CellContext`octconjugate[ Pattern[$CellContext`p$, Blank[]]] := Total[$CellContext`p$ Join[{1}, -$CellContext`octImag$$]]; Pattern[$CellContext`octConjugatePattern, SuperStar[ Pattern[$CellContext`p, Blank[]]]] := $CellContext`octconjugate[$CellContext`p]; \ $CellContext`octRe[ Pattern[$CellContext`p, Blank[]]] := Simplify[ Chop[($CellContext`octonion[$CellContext`p] + SuperStar[$CellContext`p])/2]]; $CellContext`octIm[ Pattern[$CellContext`p, Blank[]]] := Simplify[ Chop[($CellContext`octonion[$CellContext`p] - SuperStar[$CellContext`p])/2]]; $CellContext`octAbs[ Pattern[$CellContext`p, Blank[]]] := Total[{ SmallCircle[ $CellContext`octonion[$CellContext`p], SuperStar[$CellContext`p]]}]; $CellContext`octNorm[ Pattern[$CellContext`p, Blank[]]] := Sqrt[ $CellContext`octAbs[$CellContext`p]]; $CellContext`octDiv[ Pattern[$CellContext`p, Blank[]]] := Simplify[ SuperStar[$CellContext`p]/$CellContext`octAbs[$CellContext`p]]; \ $CellContext`setFM[ Pattern[$CellContext`p$, Blank[]], Pattern[$CellContext`flip$, Blank[]]] := $CellContext`fM[ First[ Apply[$CellContext`getTriads, Part[{$CellContext`invMask$$, $CellContext`altMask$$, \ $CellContext`fPi$$, $CellContext`sm$$, $CellContext`fpC$$, \ $CellContext`fpG$$} = $CellContext`pTriad[$CellContext`p$, \ $CellContext`flip$], Span[1, 4]]]]]; CircleDot[ Pattern[$CellContext`a, Blank[]], Pattern[$CellContext`b, Blank[]]] := ($CellContext`setFM[$CellContext`a, True]; SmallCircle[ $CellContext`octonion[ $CellContext`pPhys[$CellContext`a]], $CellContext`octonion[ $CellContext`pPhys[$CellContext`b]]]); \ $CellContext`fanoLines := Flatten[ Map[Partition[#, 2, 1]& , Map[($CellContext`lj = 0; $CellContext`li = #; While[ And[Increment[$CellContext`lj] < 4, Not[ Apply[Equal, Flatten[ Map[Map[Normalize, Differences[{ Part[$CellContext`coords2, Part[#, 1]], Part[$CellContext`coords2, Part[#, 2]]}]]& , Partition[$CellContext`li, 2, 1]], 1]]]], $CellContext`li = RotateRight[$CellContext`li]]; $CellContext`li)& , DeleteCases[ Map[$CellContext`basis, $CellContext`triads], Apply[Alternatives, Permutations[$CellContext`ca1]]]]], 1]; $CellContext`dskClr[ Pattern[$CellContext`p$, Blank[]]] := If[ MemberQ[{$CellContext`n1$$, $CellContext`n2$$, \ $CellContext`n3$$}, $CellContext`basisRev[$CellContext`p$]], Yellow, Cyan]; $CellContext`doArrows[ Pattern[$CellContext`in, Blank[]]] := Map[{ Lighter[Gray], If[$CellContext`in, Arrow[{ Part[$CellContext`coords2, Part[#, 1]], Part[$CellContext`coords2, Part[#, 2]]}], Cylinder[{ Part[$CellContext`coords3, Part[#, 1]], Part[$CellContext`coords3, Part[#, 2]]}, 0.03]]}& , $CellContext`fanoLines]; $CellContext`node[ Pattern[$CellContext`in, Blank[]], Pattern[$CellContext`p, Blank[]]] := { $CellContext`dskClr[$CellContext`p], EdgeForm[Black], If[$CellContext`in, Disk[ Part[$CellContext`coords2, $CellContext`p], 0.1], Sphere[ Part[$CellContext`coords3, $CellContext`p], 0.1]], Text[ Style[ Part[ If[$CellContext`in, $CellContext`octString, \ $CellContext`oct], $CellContext`basisRev[$CellContext`p]], { Black, Larger, Bold, If[$CellContext`localize, Small, Medium]}], Part[ If[$CellContext`in, $CellContext`coords2, \ $CellContext`coords3], $CellContext`p]]}; $CellContext`fanoPlane := Tooltip[ Row[{ Labeled["Fano plane", Graphics[{ Arrowheads[{{0.07, 0.7}}], $CellContext`doArrows[True], Darker[Gray], Arrowheads[{{0.07, 0.37}, {0.07, 0.68}, {0.07, 0.03}}], Arrow[ Table[ Part[$CellContext`coords2, 4] + Norm[Part[$CellContext`coords2, 3] - Part[$CellContext`coords2, 4]] { Cos[$CellContext`a], $CellContext`firstFlipSign Sin[$CellContext`a]}, {$CellContext`a, 0, 2 Pi, Pi/32}]], Map[$CellContext`node[True, #]& , Range[7]]}, ImageSize -> $CellContext`imageSize/3]]}], Text[ Grid[{{ $CellContext`pDisp[$CellContext`oct2p]}, { $CellContext`pToolTipTxt[$CellContext`oct2p]}}]]]; \ $CellContext`fanoCube := Labeled["Fano cube", Graphics3D[{ Specularity[White, $CellContext`specularity], $CellContext`doArrows[False], White, Map[Cylinder[{ Part[$CellContext`coords3, Part[#, 1]], Part[$CellContext`coords3, Part[#, 2]]}, 0.03]& , $CellContext`ca2], Map[$CellContext`node[False, #]& , Range[8]], $CellContext`txt[ "\[DoubleStruckCapitalR]\nReal", Part[$CellContext`coords3, $CellContext`basis[8]] - {2, -1, 1}/10], $CellContext`txt[ "\[DoubleStruckCapitalC]\nComplex", Part[$CellContext`coords3, $CellContext`basis[1]] - {3, 0, 1}/10], $CellContext`txt[ "\[DoubleStruckCapitalH]\nQuaternion", Part[$CellContext`coords3, $CellContext`basis[3]] - {2, -2, 1}/10], $CellContext`txt[ "\[DoubleStruckCapitalO]\nOctonion", Part[$CellContext`coords3, $CellContext`basis[7]] - {3, -1, 1}/10]}, Boxed -> False, ViewPoint -> {1., 1.2, 1.4}, ImageSize -> $CellContext`imageSize/ 3]]; $CellContext`odd4Graph := Labeled["Coxeter odd 4", Graphics[ GraphPlot[$CellContext`odd4Edges, VertexCoordinateRules -> Table[Part[$CellContext`triple35Lst, Part[$CellContext`odd4Hamiltonian, $CellContext`n]] -> { Sin[2 Pi ($CellContext`n/35)], Cos[2 Pi ($CellContext`n/35)]}, {$CellContext`n, 1, 35}], EdgeRenderingFunction -> (If[ And[Intersection[ Apply[List, #2], Part[$CellContext`fano30Triads, $CellContext`fPi$$]] == \ {}, Intersection[ Apply[List, #2], Part[$CellContext`fano30Triads, $CellContext`fPi$$]] == \ {}], {Black, Line[#]}, { If[ MemberQ[$CellContext`hoffmanSingleton, \ $CellContext`fPi$$], Yellow, Cyan], Line[#]}]& ), ImageSize -> $CellContext`imageSize/3]]]; Text[ Grid[{ $CellContext`dispTriad[$CellContext`invMask$$, \ $CellContext`altMask$$, $CellContext`fPi$$, $CellContext`sm$$, \ $CellContext`fpC$$, $CellContext`fpG$$], {$CellContext`fanoPlane, \ $CellContext`fanoCube}, { Grid[{{ Column[{SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], HoldForm[ Evaluate[ Part[$CellContext`oct, $CellContext`n2$$]]]] == SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], Part[$CellContext`oct, $CellContext`n2$$]], SmallCircle[ Part[$CellContext`oct, $CellContext`n2$$], HoldForm[ Evaluate[ Part[$CellContext`oct, $CellContext`n3$$]]]] == SmallCircle[ Part[$CellContext`oct, $CellContext`n2$$], Part[$CellContext`oct, $CellContext`n3$$]]}, Center], Column[{ Row[{"associator algebra"}], Style[SmallCircle[ SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], HoldForm[ Evaluate[ Part[$CellContext`oct, $CellContext`n2$$]]]], Part[$CellContext`oct, $CellContext`n3$$]] - SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], SmallCircle[ HoldForm[ Evaluate[ Part[$CellContext`oct, $CellContext`n2$$]]], Part[$CellContext`oct, $CellContext`n3$$]]] == \ $CellContext`associator[ Part[$CellContext`oct, $CellContext`n1$$], Part[$CellContext`oct, $CellContext`n2$$], Part[$CellContext`oct, $CellContext`n3$$]]]}, Center]}, { Column[{$CellContext`fmDispN, "numeric multiplication table"}, Center], Column[{$CellContext`fmDisp\[ScriptE], Row[{$CellContext`align, "symbolic multiplication table", $CellContext`align}]}, Center]}}], Column[{SmallCircle[ SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], HoldForm[ Evaluate[ Part[$CellContext`oct, $CellContext`n2$$]]]], Part[$CellContext`oct, $CellContext`n3$$]] == SmallCircle[ SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], Part[$CellContext`oct, $CellContext`n2$$]], Part[$CellContext`oct, $CellContext`n3$$]], SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], SmallCircle[ Part[$CellContext`oct, $CellContext`n2$$], HoldForm[ Evaluate[ Part[$CellContext`oct, $CellContext`n3$$]]]]] == SmallCircle[ Part[$CellContext`oct, $CellContext`n1$$], SmallCircle[ Part[$CellContext`oct, $CellContext`n2$$], Part[$CellContext`oct, $CellContext`n3$$]]], \ $CellContext`odd4Graph}]}, { Column[{"octonion math examples", Row[{"a=", $CellContext`octonion[$CellContext`o1]}], Row[{"b=", $CellContext`octonion[$CellContext`o2]}], Row[{"\!\(\*SuperscriptBox[\(a\), \(*\)]\)=", SuperStar[$CellContext`o1]}], Row[{"a\[SmallCircle]b=", SmallCircle[ $CellContext`octonion[$CellContext`o1], $CellContext`octonion[$CellContext`o2]]}], Row[{"\[RightDoubleBracketingBar]ab\ \[RightDoubleBracketingBar]=\[RightDoubleBracketingBar]a\ \[RightDoubleBracketingBar] \[RightDoubleBracketingBar]b\ \[RightDoubleBracketingBar]=\!\(\*SqrtBox[\(\*SuperscriptBox[\(a\), \(*\)] \ a\)]\)\!\(\*SqrtBox[\(\*SuperscriptBox[\(b\), \(*\)] b\)]\)=", \ $CellContext`octNorm[$CellContext`o1] $CellContext`octNorm[$CellContext`o2]}], Row[{"a\[SmallCircle]b-b\[SmallCircle]a=", $CellContext`commutator[ $CellContext`octonion[$CellContext`o1], $CellContext`octonion[$CellContext`o2]]}], Row[{"\!\(\*FractionBox[\(1\), \(a\)]\)=", $CellContext`octDiv[$CellContext`o1]}]}]}}, Alignment -> { Left, Top}]]]], $CellContext`localFano = {$CellContext`d8Q, \ $CellContext`excFanoQ, $CellContext`doD8, $CellContext`oct2p, \ $CellContext`fM, $CellContext`fm, $CellContext`triads, \ $CellContext`flatFanoStyled, $CellContext`flatFano, \ $CellContext`firstFlipSign, $CellContext`chkOctStyle, $CellContext`octPM, \ $CellContext`pmChk, $CellContext`posChk, $CellContext`fanoChk, \ $CellContext`fmTable, $CellContext`fmDispN, $CellContext`fmDisp\[ScriptE], \ $CellContext`basis, $CellContext`basisRev, $CellContext`fanoLines, \ $CellContext`dskClr, $CellContext`associator, $CellContext`octonion, \ $CellContext`commutator, $CellContext`octconjugate, $CellContext`octRe, \ $CellContext`octIm, $CellContext`octAbs, $CellContext`octNorm, \ $CellContext`octDiv, $CellContext`setFM, $CellContext`doArrows, \ $CellContext`node, $CellContext`fanoPlane, $CellContext`fanoCube, \ $CellContext`odd4Graph}, $CellContext`fpD8 = {2, 5, 9, 7, 10, 12, 13, 15, 19, 20, 21, 23, 26, 29, 28}, $CellContext`fpC8 = {1, 3, 6, 4, 8, 11, 14, 16, 17, 18, 22, 24, 25, 27, 30}, $CellContext`fB[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`bit, Blank[]]] := BitAnd[ Abs[$CellContext`p], $CellContext`bit], $CellContext`spConv[ Pattern[$CellContext`anti, Blank[]], Pattern[$CellContext`prt, Blank[]], Pattern[$CellContext`clr, Blank[]], Pattern[$CellContext`sp, Blank[]]] := $CellContext`position[$CellContext`e8Orig, If[$CellContext`anti, Subtract, Plus][0, Part[$CellContext`e8Orig, $CellContext`basePos[$CellContext`prt, $CellContext`clr, \ $CellContext`sp]]]], $CellContext`position[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := $CellContext`first[ Flatten[ Position[$CellContext`x, $CellContext`y, 1, Heads -> False]]], $CellContext`first[ Pattern[$CellContext`in, Blank[]]] := If[Length[$CellContext`in] == 0, $CellContext`in, First[$CellContext`in]], $CellContext`e8Orig = {{(-1)/2, (-1)/ 2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, {0, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, -1, 0}, {0, 0, 0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, -1, 0, 0, 0}, {0, 0, 0, -1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0, 0, 0}, {0, -1, 0, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0, 0, 0}, { 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, 1/ 2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, 1/ 2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, 1/ 2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2}, {(-1)/2, 1/ 2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2}, {(-1)/2, 1/ 2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, 1/ 2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, 1/ 2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, 1/ 2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, 1/ 2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, (-1)/2, 1/ 2, (-1)/2, 1/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, (-1)/2, 1/ 2, (-1)/2, (-1)/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, (-1)/2, 1/ 2, (-1)/2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/ 2, (-1)/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/ 2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/ 2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2}, {-1, -1, 0, 0, 0, 0, 0, 0}, {-1, 0, -1, 0, 0, 0, 0, 0}, {-1, 0, 0, -1, 0, 0, 0, 0}, {-1, 0, 0, 0, -1, 0, 0, 0}, {-1, 0, 0, 0, 0, -1, 0, 0}, {-1, 0, 0, 0, 0, 0, -1, 0}, {-1, 0, 0, 0, 0, 0, 0, -1}, {-1, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, 0, 0, 1, 0}, {-1, 0, 0, 0, 0, 1, 0, 0}, {-1, 0, 0, 0, 1, 0, 0, 0}, {-1, 0, 0, 1, 0, 0, 0, 0}, {-1, 0, 1, 0, 0, 0, 0, 0}, {-1, 1, 0, 0, 0, 0, 0, 0}, {0, -1, -1, 0, 0, 0, 0, 0}, {0, -1, 0, -1, 0, 0, 0, 0}, { 0, -1, 0, 0, -1, 0, 0, 0}, {0, -1, 0, 0, 0, -1, 0, 0}, {0, -1, 0, 0, 0, 0, -1, 0}, {0, -1, 0, 0, 0, 0, 0, -1}, {0, -1, 0, 0, 0, 0, 0, 1}, {0, -1, 0, 0, 0, 0, 1, 0}, {0, -1, 0, 0, 0, 1, 0, 0}, {0, -1, 0, 0, 1, 0, 0, 0}, {0, -1, 0, 1, 0, 0, 0, 0}, {0, -1, 1, 0, 0, 0, 0, 0}, {0, 0, -1, -1, 0, 0, 0, 0}, {0, 0, -1, 0, -1, 0, 0, 0}, {0, 0, -1, 0, 0, -1, 0, 0}, {0, 0, -1, 0, 0, 0, -1, 0}, {0, 0, -1, 0, 0, 0, 0, -1}, {0, 0, -1, 0, 0, 0, 0, 1}, {0, 0, -1, 0, 0, 0, 1, 0}, {0, 0, -1, 0, 0, 1, 0, 0}, {0, 0, -1, 0, 1, 0, 0, 0}, {0, 0, -1, 1, 0, 0, 0, 0}, {0, 0, 0, -1, -1, 0, 0, 0}, {0, 0, 0, -1, 0, -1, 0, 0}, {0, 0, 0, -1, 0, 0, -1, 0}, {0, 0, 0, -1, 0, 0, 0, -1}, {0, 0, 0, -1, 0, 0, 0, 1}, {0, 0, 0, -1, 0, 0, 1, 0}, {0, 0, 0, -1, 0, 1, 0, 0}, {0, 0, 0, -1, 1, 0, 0, 0}, {0, 0, 0, 0, -1, -1, 0, 0}, {0, 0, 0, 0, -1, 0, -1, 0}, {0, 0, 0, 0, -1, 0, 0, -1}, {0, 0, 0, 0, -1, 0, 0, 1}, {0, 0, 0, 0, -1, 0, 1, 0}, {0, 0, 0, 0, -1, 1, 0, 0}, {0, 0, 0, 0, 0, -1, -1, 0}, {0, 0, 0, 0, 0, -1, 0, -1}, {0, 0, 0, 0, 0, -1, 0, 1}, {0, 0, 0, 0, 0, -1, 1, 0}, {0, 0, 0, 0, 0, 0, -1, -1}, {0, 0, 0, 0, 0, 0, -1, 1}, { 1/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2}, { 1/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2}, { 1/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2}, { 1/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2}, { 1/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2}, { 1/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2}, { 1/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2}, { 1/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2}, { 1/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2}, { 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2}, { 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2}, { 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2}, { 1/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2}, { 1/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2}, { 1/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2}, { 1/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2}, { 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2}, { 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2}, { 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2}, { 1/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2}, { 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2}, { 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2}, { 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2}, {(-1)/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2, (-1)/2}, {(-1)/2, 1/2, 1/2, 1/ 2, (-1)/2, 1/2, (-1)/2, (-1)/2}, {(-1)/2, 1/2, 1/2, 1/2, (-1)/ 2, (-1)/2, 1/2, (-1)/2}, {(-1)/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/ 2, (-1)/2, 1/2}, {(-1)/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/ 2, (-1)/2}, {(-1)/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/ 2}, {(-1)/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2}, {(-1)/2, 1/2, 1/ 2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2}, {(-1)/2, 1/2, 1/2, (-1)/ 2, (-1)/2, (-1)/2, 1/2, 1/2}, {(-1)/2, 1/2, (-1)/2, 1/2, 1/2, 1/ 2, (-1)/2, (-1)/2}, {(-1)/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/ 2, (-1)/2}, {(-1)/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/ 2}, {(-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2}, {(-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2}, {(-1)/2, 1/2, (-1)/ 2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2}, {(-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2}, {(-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/ 2, (-1)/2, 1/2}, {(-1)/2, 1/2, (-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2}, {(-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2}, {(-1)/ 2, (-1)/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2}, {(-1)/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, 1/2, 1/2, 1/ 2, (-1)/2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/ 2}, {(-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2}, {(-1)/ 2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2}, {(-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2}, {(-1)/2, (-1)/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2}, {(-1)/2, (-1)/2, 1/2, (-1)/2, (-1)/2, 1/ 2, 1/2, 1/2}, {(-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, (-1)/ 2}, {(-1)/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2, 1/2}, {(-1)/ 2, (-1)/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, 1/2}, {(-1)/2, (-1)/ 2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, 1/2}, {(-1)/2, (-1)/2, (-1)/ 2, (-1)/2, 1/2, 1/2, 1/2, 1/2}, {0, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 1, -1, 0}, {0, 0, 0, 0, 0, 1, 0, -1}, {0, 0, 0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 1, -1, 0, 0}, {0, 0, 0, 0, 1, 0, -1, 0}, {0, 0, 0, 0, 1, 0, 0, -1}, {0, 0, 0, 0, 1, 0, 0, 1}, {0, 0, 0, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 1, -1, 0, 0, 0}, {0, 0, 0, 1, 0, -1, 0, 0}, {0, 0, 0, 1, 0, 0, -1, 0}, {0, 0, 0, 1, 0, 0, 0, -1}, {0, 0, 0, 1, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 1, -1, 0, 0, 0, 0}, {0, 0, 1, 0, -1, 0, 0, 0}, {0, 0, 1, 0, 0, -1, 0, 0}, {0, 0, 1, 0, 0, 0, -1, 0}, {0, 0, 1, 0, 0, 0, 0, -1}, {0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0}, {0, 1, -1, 0, 0, 0, 0, 0}, {0, 1, 0, -1, 0, 0, 0, 0}, {0, 1, 0, 0, -1, 0, 0, 0}, {0, 1, 0, 0, 0, -1, 0, 0}, {0, 1, 0, 0, 0, 0, -1, 0}, {0, 1, 0, 0, 0, 0, 0, -1}, {0, 1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 1, 0}, {0, 1, 0, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 0, 0}, {1, -1, 0, 0, 0, 0, 0, 0}, {1, 0, -1, 0, 0, 0, 0, 0}, {1, 0, 0, -1, 0, 0, 0, 0}, {1, 0, 0, 0, -1, 0, 0, 0}, {1, 0, 0, 0, 0, -1, 0, 0}, {1, 0, 0, 0, 0, 0, -1, 0}, {1, 0, 0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 1, 0, 0}, {1, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0, 0, 0}, { 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2}, { 1/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2}, { 1/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2}, { 1/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2}, { 1/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2}, { 1/2, 1/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2}, { 1/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2}, { 1/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2}, { 1/2, 1/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2}, { 1/2, 1/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2}, { 1/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, (-1)/2}, { 1/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2, 1/2}, { 1/2, 1/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, 1/2}, { 1/2, 1/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, 1/2}, { 1/2, 1/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, 1/2}, { 1/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, (-1)/2}, { 1/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, 1/2}, { 1/2, (-1)/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, 1/2}, { 1/2, (-1)/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, 1/2}, { 1/2, (-1)/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, 1/2}, { 1/2, (-1)/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2}, {(-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, (-1)/2}, {(-1)/2, 1/2, 1/2, 1/2, 1/2, 1/ 2, (-1)/2, 1/2}, {(-1)/2, 1/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, 1/ 2}, {(-1)/2, 1/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, 1/2}, {(-1)/2, 1/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, 1/2}, {(-1)/2, 1/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2}, {(-1)/2, (-1)/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2}, { 1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/ 2}}, $CellContext`basePos[ Pattern[$CellContext`prt, Blank[]], Pattern[$CellContext`clr, Blank[]], Pattern[$CellContext`sp, Blank[]]] := Subscript[ Underscript[ Part[ Flatten[$CellContext`flavorList], $CellContext`position[ Flatten[$CellContext`flavorListStr], ReplaceAll[$CellContext`prt, $CellContext`qConvDoNoAnti]]], If[$CellContext`clr == "\" \"", $CellContext`clr, Part[$CellContext`colorListExp, $CellContext`position[$CellContext`colorList, \ $CellContext`clr]]]], $CellContext`sp], Attributes[Subscript] = {NHoldRest}, Subscript[$CellContext`F, Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`l, Blank[]]][ Pattern[$CellContext`r, Blank[]]] := ($CellContext`r^$CellContext`l Factorial[$CellContext`n + $CellContext`l] LaguerreL[$CellContext`n - $CellContext`l - 1, 2 $CellContext`l + 1, $CellContext`r])/E^($CellContext`r/2), Subscript[$CellContext`R, Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`l, Blank[]]][ Pattern[$CellContext`r, Blank[]]] := (2/($CellContext`n $CellContext`a0))^2 Sqrt[($CellContext`a0/4) ( Factorial[$CellContext`n - $CellContext`l - 1]/ Factorial[$CellContext`n + $CellContext`l]^3)] Subscript[$CellContext`F, $CellContext`n, $CellContext`l][( 2 $CellContext`r)/($CellContext`n $CellContext`a0)], Subscript[$CellContext`Y, Pattern[$CellContext`l, Blank[]], Pattern[$CellContext`m, Blank[]]][ Pattern[$CellContext`\[Theta], Blank[]], Pattern[$CellContext`\[Phi], Blank[]]] := SphericalHarmonicY[$CellContext`l, $CellContext`m, $CellContext`\ \[Theta], $CellContext`\[Phi]], Subscript[$CellContext`\[Psi], Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`l, Blank[]], Pattern[$CellContext`m, Blank[]]][ Pattern[$CellContext`r, Blank[]], Pattern[$CellContext`\[Theta], Blank[]], Pattern[$CellContext`\[Phi], Blank[]]] := ($CellContext`\[HBar]/2) Subscript[$CellContext`R, $CellContext`n, \ $CellContext`l][$CellContext`r] Abs[ Subscript[$CellContext`Y, $CellContext`l, \ $CellContext`m][$CellContext`\[Theta], $CellContext`\[Phi]]], Subscript[$CellContext`\[Psi]2, Pattern[$CellContext`n, Blank[]], Pattern[$CellContext`l, Blank[]], Pattern[$CellContext`m, Blank[]]][ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Module[{$CellContext`r = Norm[{$CellContext`x, $CellContext`y}]}, Subscript[$CellContext`\[Psi], $CellContext`n, $CellContext`l, \ $CellContext`m][$CellContext`r, ArcCos[$CellContext`y/$CellContext`r], ArcTan[$CellContext`x, 0]]^2], Subscript[$CellContext`R, Infinity] = $CellContext`FineStructureConstant, Pattern[$CellContext`scaledPattern, Subscript[ Pattern[$CellContext`p, Blank[]], $CellContext`scaled]] := $CellContext`p \ $CellContext`zoomFct, Pattern[$CellContext`tinyPattern, Subscript[ Pattern[$CellContext`x, Blank[]], $CellContext`tiny]] := {$CellContext`x, 2/4}, Pattern[$CellContext`smallPattern, Subscript[ Pattern[$CellContext`x, Blank[]], $CellContext`small]] := {$CellContext`x, 3/4}, Pattern[$CellContext`nrmlPattern, Subscript[ Pattern[$CellContext`x, Blank[]], $CellContext`nrml]] := {$CellContext`x, 4/4}, Pattern[$CellContext`bigPattern, Subscript[ Pattern[$CellContext`x, Blank[]], $CellContext`big]] := {$CellContext`x, 5/4}, Pattern[$CellContext`hugePattern, Subscript[ Pattern[$CellContext`x, Blank[]], $CellContext`huge]] := {$CellContext`x, 6/4}, Pattern[$CellContext`varPattern$, Subscript[ Pattern[$CellContext`x$, Blank[]], $CellContext`varS]] := Subscript[$CellContext`x$, Hold[$CellContext`pSize$$]], Pattern[$CellContext`spinLuPattern, Subscript[ Pattern[$CellContext`prt, Blank[]], Overscript[ "L", "\[Vee]"]]] := $CellContext`position[$CellContext`e8bit, $CellContext`pBit[$CellContext`prt]], Pattern[$CellContext`spinLdPattern, Subscript[ Pattern[$CellContext`prt, Blank[]], Overscript[ "R", "\[Wedge]"]]] := $CellContext`position[$CellContext`e8bit, \ $CellContext`pBit[$CellContext`prt] + 2^Part[$CellContext`bOrd, 4]], Pattern[$CellContext`spinRuPattern, Subscript[ Pattern[$CellContext`prt, Blank[]], Overscript[ "L", "\[Wedge]"]]] := $CellContext`position[$CellContext`e8bit, \ $CellContext`pBit[$CellContext`prt] + 2^(Part[$CellContext`bOrd, 4] + 1)], Pattern[$CellContext`spinRdPattern, Subscript[ Pattern[$CellContext`prt, Blank[]], Overscript[ "R", "\[Vee]"]]] := $CellContext`position[$CellContext`e8bit, \ $CellContext`pBit[$CellContext`prt] + 2^Part[$CellContext`bOrd, 4] + 2^(Part[$CellContext`bOrd, 4] + 1)], $CellContext`l = {183, 192, 203, 48, 244, 238, 233, 229, 94, 23, 18, 12, 72, 81, 216, 61, 148, 128, 162, 158, 10, 1, 17, 11}, $CellContext`a0 = 1/(4 Pi), $CellContext`\[HBar] = 1/(2 Pi), $CellContext`zoomFct := 1. 10^$CellContext`zoom$$, Attributes[Overscript] = {NHoldRest}, Overscript[$CellContext`l1, Blank[]] = {74, 13, 163}, Overscript[$CellContext`l2, Blank[]] = {185, 109, 247}, Overscript[{183, 192, 203, 48, 244, 238, 233, 229, 94, 23, 18, 12, 72, 81, 216, 61, 148, 128, 162, 158, 10, 1, 17, 11}, Blank[]] = {74, 65, 54, 209, 13, 19, 24, 28, 163, 234, 239, 245, 185, 176, 41, 196, 109, 129, 95, 99, 247, 256, 240, 246}, Overscript[$CellContext`q1, Blank[]] = {191, 14, 32}, Overscript[$CellContext`q2, Blank[]] = {80, 110, 149}, Overscript[{66, 75, 210, 55, 67, 76, 211, 56, 68, 77, 212, 57, 243, 237, 232, 228, 242, 236, 231, 227, 241, 235, 230, 226, 225, 154, 144, 124, 224, 153, 143, 123, 223, 152, 142, 122, 177, 186, 197, 42, 178, 187, 198, 43, 179, 188, 199, 44, 147, 127, 161, 157, 146, 126, 160, 156, 145, 125, 159, 155, 108, 37, 138, 118, 107, 36, 137, 117, 106, 35, 136, 116}, Blank[]] = {191, 182, 47, 202, 190, 181, 46, 201, 189, 180, 45, 200, 14, 20, 25, 29, 15, 21, 26, 30, 16, 22, 27, 31, 32, 103, 113, 133, 33, 104, 114, 134, 34, 105, 115, 135, 80, 71, 60, 215, 79, 70, 59, 214, 78, 69, 58, 213, 110, 130, 96, 100, 111, 131, 97, 101, 112, 132, 98, 102, 149, 220, 119, 139, 150, 221, 120, 140, 151, 222, 121, 141}, Overscript[$CellContext`\[Omega]g1, Blank[]] = {167, 166, 164}, Overscript[$CellContext`\[Omega]g2, Blank[]] = {64, 206, 38}, Overscript[{90, 91, 93, 193, 51, 219}, Blank[]] = {167, 166, 164, 64, 206, 38}, Overscript[$CellContext`\[Phi]\[CapitalPhi]1, Blank[]] = {170, 171, 172}, Overscript[$CellContext`\[Phi]\[CapitalPhi]2, Blank[]] = {53, 50, 40}, Overscript[{87, 92, 175, 86, 89, 174, 85, 88, 173, 204, 195, 218, 207, 205, 194, 217, 49, 73}, Blank[]] = {170, 165, 82, 171, 168, 83, 172, 169, 84, 53, 62, 39, 50, 52, 63, 40, 208, 184}, Overscript[ Subscript[$CellContext`Ex, 1], Blank[]] = 2, Overscript[$CellContext`ex1, Blank[]] = 2, Overscript[ Subscript[$CellContext`Ex, 2], Blank[]] = 6, Overscript[$CellContext`ex2, Blank[]] = 6, Overscript[{255, 254, 253, 252, 251, 250, 249, 248}, Blank[]] = {2, 3, 4, 5, 6, 7, 8, 9}, $CellContext`l1 = {183, 244, 94}, $CellContext`l2 = {72, 148, 10}, $CellContext`q1 = {66, 243, 225}, $CellContext`q2 = {177, 147, 108}, $CellContext`\[Omega]g1 = { 90, 91, 93}, $CellContext`\[Omega]g2 = {193, 51, 219}, $CellContext`\[Phi]\[CapitalPhi]1 = {87, 86, 85}, $CellContext`\[Phi]\[CapitalPhi]2 = {204, 207, 217}, $CellContext`ex1 = 2, $CellContext`ex2 = 6, $CellContext`e8bit = {71, 128, 132, 136, 140, 192, 196, 200, 204, 67, 79, 15, 130, 146, 162, 178, 75, 11, 134, 150, 166, 182, 7, 138, 154, 170, 186, 142, 158, 174, 190, 147, 163, 179, 119, 103, 87, 252, 216, 240, 201, 93, 109, 125, 185, 169, 153, 13, 116, 224, 108, 228, 208, 137, 29, 45, 61, 249, 233, 217, 77, 212, 232, 220, 133, 17, 33, 49, 245, 229, 213, 65, 120, 129, 21, 37, 53, 241, 225, 209, 69, 152, 168, 184, 48, 32, 16, 52, 36, 28, 44, 20, 60, 3, 202, 218, 234, 250, 206, 222, 238, 254, 151, 167, 183, 115, 99, 83, 194, 210, 226, 242, 155, 171, 187, 127, 111, 95, 219, 235, 251, 63, 47, 31, 118, 102, 86, 70, 198, 214, 230, 246, 159, 175, 191, 123, 107, 91, 223, 239, 255, 59, 43, 27, 114, 98, 82, 66, 211, 227, 243, 55, 39, 23, 126, 110, 94, 78, 122, 106, 90, 74, 131, 188, 148, 172, 156, 164, 180, 144, 160, 176, 56, 40, 24, 197, 81, 97, 113, 181, 165, 149, 1, 248, 193, 85, 101, 117, 177, 161, 145, 5, 92, 104, 84, 205, 89, 105, 121, 189, 173, 157, 9, 80, 100, 236, 96, 244, 141, 25, 41, 57, 253, 237, 221, 73, 112, 88, 124, 215, 231, 247, 51, 35, 19, 62, 46, 30, 14, 58, 42, 26, 10, 135, 54, 38, 22, 6, 139, 203, 50, 34, 18, 2, 143, 207, 195, 76, 72, 68, 64, 12, 8, 4, 0, 199}, $CellContext`pBit[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, Min[$CellContext`p, 256], $CellContext`sets + 2], $CellContext`e8b = {{1, 71, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "l"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {2, 128, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "+"]]], {"y", "d"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {3, 132, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "+"]]], {"y", "l"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {4, 136, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "+"]]], {"y", "m"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {5, 140, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "+"]]], {"y", "m"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {6, 192, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "d"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {7, 196, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "l"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {8, 200, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {9, 204, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, Subscript[$CellContext`inv, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {10, 67, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "d"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {11, 79, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {12, 15, HoldForm[HoldForm[ Underoverscript["\[Tau]", Subscript["y", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "-"]]], { "y", "m"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1776.99, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[ 2.9060100000000007`*^-13, 10, NumberPadding -> {" ", "0"}], " s"}]}, {13, 130, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "+"]]], { "y", "d"}, {$CellContext`utr, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {14, 146, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "o", "d"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {15, 162, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "c", "d"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {16, 178, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "m", "d"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {17, 75, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {18, 11, HoldForm[HoldForm[ Underoverscript["\[Tau]", Subscript["y", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "-"]]], { "y", "m"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1776.99, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[ 2.9060100000000007`*^-13, 10, NumberPadding -> {" ", "0"}], " s"}]}, {19, 134, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "+"]]], { "y", "l"}, {$CellContext`utr, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {20, 150, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`1\/3\)"]]], { "o", "l"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {21, 166, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`1\/3\)"]]], { "c", "l"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {22, 182, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`1\/3\)"]]], { "m", "l"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {23, 7, HoldForm[HoldForm[ Underoverscript["\[Tau]", Subscript["y", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "-"]]], { "y", "l"}, {$CellContext`tri, 3/2}, 1, Row[{ NumberForm[1776.99, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[ 2.9060100000000007`*^-13, 10, NumberPadding -> {" ", "0"}], " s"}]}, {24, 138, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "+"]]], { "y", "m"}, {$CellContext`utr, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ 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NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {28, 142, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "+"]]], { "y", "m"}, {$CellContext`utr, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {29, 158, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "o", "m"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {30, 174, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "c", "m"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {31, 190, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "m", "m"}, {$CellContext`dia, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {32, 147, HoldForm[HoldForm[ Underoverscript["b", Subscript["o", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "o", "d"}, {$CellContext`dia, 3/2}, 2, Row[{ NumberForm[4200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {33, 163, HoldForm[HoldForm[ Underoverscript["b", Subscript["c", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "c", "d"}, {$CellContext`dia, 3/2}, 2, Row[{ NumberForm[4200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {34, 179, HoldForm[HoldForm[ Underoverscript["b", Subscript["m", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`1\/3\)"]]], { "m", "d"}, {$CellContext`dia, 3/2}, 2, Row[{ NumberForm[4200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {35, 119, HoldForm[HoldForm[ Underoverscript["t", Subscript["b", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`2\/3\)"]]], { "b", "l"}, {$CellContext`squ, 3/2}, 2, Row[{ NumberForm[174200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {36, 103, HoldForm[HoldForm[ Underoverscript["t", Subscript["g", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", 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Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(2\/3\)\)\)\)"]]], { "r", "l"}, {$CellContext`dia, 3/2}, 2, Row[{ NumberForm[174200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {221, 231, HoldForm[HoldForm[ Underoverscript["t", Subscript["g", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(2\/3\)\)\)\)"]]], { "g", "l"}, {$CellContext`dia, 3/2}, 2, Row[{ NumberForm[174200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {222, 247, HoldForm[HoldForm[ Underoverscript["t", Subscript["b", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(2\/3\)\)\)\)"]]], { "b", "l"}, {$CellContext`dia, 3/2}, 2, Row[{ NumberForm[174200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {223, 51, HoldForm[HoldForm[ Underoverscript["b", Subscript["m", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "m", "d"}, {$CellContext`squ, 3/2}, 2, Row[{ NumberForm[4200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {224, 35, HoldForm[HoldForm[ Underoverscript["b", Subscript["c", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "c", "d"}, {$CellContext`squ, 3/2}, 2, Row[{ NumberForm[4200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {225, 19, HoldForm[HoldForm[ Underoverscript["b", Subscript["o", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "o", "d"}, {$CellContext`squ, 3/2}, 2, Row[{ NumberForm[4200., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {226, 62, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "m", "m"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {227, 46, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "c", "m"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {228, 30, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "o", "m"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {229, 14, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "-"]]], { "y", "m"}, {$CellContext`tri, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {230, 58, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "m", "m"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {231, 42, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "c", "m"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {232, 26, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "o", "m"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {233, 10, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "m"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "-"]]], { "y", "m"}, {$CellContext`tri, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {234, 135, HoldForm[HoldForm[ Underoverscript["\[Tau]", Subscript["y", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "+"]]], { "y", "l"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1776.99, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[ 2.9060100000000007`*^-13, 10, NumberPadding -> {" ", "0"}], " s"}]}, {235, 54, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "m", "l"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {236, 38, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "c", "l"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {237, 22, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "o", "l"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {238, 6, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "l"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "-"]]], { "y", "l"}, {$CellContext`tri, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {239, 139, HoldForm[HoldForm[ Underoverscript["\[Tau]", Subscript["y", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "+"]]], { "y", "m"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1776.99, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[ 2.9060100000000007`*^-13, 10, NumberPadding -> {" ", "0"}], " s"}]}, {240, 203, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {241, 50, HoldForm[HoldForm[ Underoverscript["s", Subscript["m", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "m", "d"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {242, 34, HoldForm[HoldForm[ Underoverscript["s", Subscript["c", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "c", "d"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {243, 18, HoldForm[HoldForm[ Underoverscript["s", Subscript["o", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`\(-\(\(1\/3\)\)\)\)"]]], { "o", "d"}, {$CellContext`squ, 1}, 2, Row[{ NumberForm[95., 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {244, 2, HoldForm[HoldForm[ Underoverscript["\[Mu]", Subscript["y", "d"], ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "-"]]], { "y", "d"}, {$CellContext`tri, 1}, 1, Row[{ NumberForm[105.658369, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[2.197040000001*^-6, 10, NumberPadding -> {" ", "0"}], " s"}]}, {245, 143, HoldForm[HoldForm[ Underoverscript["\[Tau]", Subscript["y", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "+"]]], { "y", "m"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1776.99, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{ NumberForm[ 2.9060100000000007`*^-13, 10, NumberPadding -> {" ", "0"}], " s"}]}, {246, 207, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "m"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {247, 195, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "d"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "d"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {248, 76, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {249, 72, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "m"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {250, 68, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "l"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {251, 64, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "2"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "\!\(TraditionalForm\`0\)"]]], { "w", "d"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {252, 12, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Vee]"], "-"]]], {"y", "m"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {253, 8, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Wedge]"], "-"]]], {"y", "m"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {254, 4, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "-"]]], {"y", "l"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {255, 0, HoldForm[HoldForm[ Underoverscript[ Subscript["Ex", "1"], "\" \"", ""]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["L", "\[Vee]"], "-"]]], {"y", "d"}, Subscript[$CellContext`cir, Hold[$CellContext`pSize$$]], 5, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}, {256, 199, HoldForm[HoldForm[ Underoverscript[ Subscript["\[Nu]", "\[Tau]"], Subscript["w", "l"], Blank[]]] HoldForm[ Subsuperscript[ Invisible[$CellContext`\[VerticalLine]], Overscript["R", "\[Wedge]"], "\!\(TraditionalForm\`0\)"]]], { "w", "l"}, {$CellContext`utr, 3/2}, 1, Row[{ NumberForm[1.*^-18, 10, NumberPadding -> {" ", "0"}], " MeV"}], Row[{"?", " s"}]}}, Attributes[Underoverscript] = {NHoldRest}, Underoverscript[ Superscript[$CellContext`g, Row[{$CellContext`r, Overscript[$CellContext`b, Blank[]]}]], $CellContext`rb, Blank[]] = 166, Underoverscript[ Subscript[$CellContext`\[Omega], $CellContext`R], $CellContext`rb, Blank[]] = 206, Underoverscript[ Row[{ Subscript[$CellContext`x, 2], $CellContext`\[CapitalPhi]}], $CellContext`rb, Blank[]] = 171, Underoverscript[$CellContext`B, $CellContext`rb, Blank[]] = 50, Pattern[$CellContext`colorGreenPattern, Underoverscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`rb, Blank[]]] := $CellContext`position[$CellContext`e8bit, \ $CellContext`pBit[ Underoverscript[$CellContext`prt, $CellContext`bg, Blank[]]] + 2^Part[$CellContext`bOrd, 3]], Underoverscript[ Superscript[$CellContext`g, Row[{$CellContext`r, Overscript[$CellContext`g, Blank[]]}]], $CellContext`rg, Blank[]] = 164, Underoverscript[$CellContext`W, $CellContext`rg, Blank[]] = 38, Underoverscript[ Row[{ Subscript[$CellContext`x, 3], $CellContext`\[CapitalPhi]}], $CellContext`rg, Blank[]] = 172, Underoverscript[$CellContext`B, $CellContext`rg, Blank[]] = 40, Pattern[$CellContext`colorBluePattern, Underoverscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`rg, Blank[]]] := $CellContext`position[$CellContext`e8bit, \ $CellContext`pBit[ Underoverscript[$CellContext`prt, $CellContext`bg, Blank[]]] + 2^(Part[$CellContext`bOrd, 3] + 1)], Pattern[$CellContext`particlePattern, Underoverscript[ Pattern[$CellContext`prt, Blank[]], Subscript[ Pattern[$CellContext`clr, Blank[]], Pattern[$CellContext`sp, Blank[]]], Pattern[$CellContext`anti, Blank[]]]] := $CellContext`spConv[ If[$CellContext`anti == "", False, True], $CellContext`prt, $CellContext`clr, $CellContext`sp], Underoverscript[$CellContext`e, $CellContext`y, Blank[]] = 74, Underoverscript[$CellContext`\[Mu], $CellContext`y, Blank[]] = 13, Underoverscript[$CellContext`\[Tau], $CellContext`y, Blank[]] = 163, Underoverscript[ Subscript[$CellContext`\[Nu], $CellContext`e], $CellContext`y, Blank[]] = 185, Underoverscript[$CellContext`\[Nu], $CellContext`y, Blank[]] = 185, Underoverscript[ Subscript[$CellContext`\[Nu], $CellContext`\[Mu]], $CellContext`y, Blank[]] = 109, Underoverscript[ Subscript[$CellContext`\[Nu], $CellContext`\[Tau]], $CellContext`y, Blank[]] = 247, Underoverscript[$CellContext`d, $CellContext`bg, Blank[]] = 191, Underoverscript[$CellContext`s, $CellContext`bg, Blank[]] = 14, Underoverscript[$CellContext`b, $CellContext`bg, Blank[]] = 32, Underoverscript[$CellContext`u, $CellContext`bg, Blank[]] = 80, Underoverscript[$CellContext`c, $CellContext`bg, Blank[]] = 110, Underoverscript[$CellContext`t, $CellContext`bg, Blank[]] = 149, Underoverscript[ Superscript[$CellContext`g, Row[{$CellContext`g, Overscript[$CellContext`b, Blank[]]}]], $CellContext`bg, Blank[]] = 167, Underoverscript[$CellContext`g, $CellContext`bg, Blank[]] = 167, Underoverscript[ Superscript[$CellContext`g, Row[{$CellContext`r, Overscript[$CellContext`b, Blank[]]}]], $CellContext`bg, Blank[]] = 166, Underoverscript[ Superscript[$CellContext`g, Row[{$CellContext`r, Overscript[$CellContext`g, Blank[]]}]], $CellContext`bg, Blank[]] = 164, Underoverscript[ Subscript[$CellContext`\[Omega], $CellContext`L], $CellContext`bg, Blank[]] = 64, Underoverscript[$CellContext`\[Omega], $CellContext`bg, Blank[]] = 64, Underoverscript[ Subscript[$CellContext`\[Omega], $CellContext`R], $CellContext`bg, Blank[]] = 206, Underoverscript[$CellContext`W, $CellContext`bg, Blank[]] = 38, Underoverscript[ Row[{ Subscript[$CellContext`x, 1], $CellContext`\[CapitalPhi]}], $CellContext`bg, Blank[]] = 170, Underoverscript[$CellContext`\[CapitalPhi], $CellContext`bg, Blank[]] = 170, Underoverscript[ Row[{ Subscript[$CellContext`x, 2], $CellContext`\[CapitalPhi]}], $CellContext`bg, Blank[]] = 171, Underoverscript[ Row[{ Subscript[$CellContext`x, 3], $CellContext`\[CapitalPhi]}], $CellContext`bg, Blank[]] = 172, Underoverscript[ Row[{ Subscript[$CellContext`e, $CellContext`T], \ $CellContext`\[Phi]}], $CellContext`bg, Blank[]] = 53, Underoverscript[ Row[{ Subscript[$CellContext`e, $CellContext`S], \ $CellContext`\[Phi]}], $CellContext`bg, Blank[]] = 53, Underoverscript[$CellContext`\[Phi], $CellContext`bg, Blank[]] = 53, Underoverscript[$CellContext`B, $CellContext`bg, Blank[]] = 53, Underoverscript[ Subscript[$CellContext`Ex, 1], $CellContext`rgb, Blank[]] = 2, Underoverscript[ Subscript[$CellContext`Ex, 2], $CellContext`rgb, Blank[]] = 6, Attributes[Superscript] = { NHoldRest, ReadProtected}, $CellContext`bOrd = {7, 6, 4, 2, 0}, $CellContext`c = 1, Attributes[Subsuperscript] = { NHoldRest, ReadProtected}, $CellContext`tri[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := $CellContext`polyTri[$CellContext`coords, \ $CellContext`scale, Subtract, "Tetrahedron", $CellContext`plDims], $CellContext`polyTri[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`pm, Blank[]], Pattern[$CellContext`shape, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := If[$CellContext`plDims == 3, Translate[ Scale[{ PolyhedronData[$CellContext`shape, "Faces"]}, {1, 1, 1} $CellContext`scale, {0, 0, 0}], $CellContext`coords], Polygon[{{Part[$CellContext`coords, 1] - $CellContext`scale, $CellContext`pm[ Part[$CellContext`coords, 2], $CellContext`scale/Sqrt[3]]}, { Part[$CellContext`coords, 1] + $CellContext`scale, $CellContext`pm[ Part[$CellContext`coords, 2], $CellContext`scale/Sqrt[3]]}, { Part[$CellContext`coords, 1], $CellContext`pm[ Part[$CellContext`coords, 2], (-2) ($CellContext`scale/Sqrt[ 3])]}}]], $CellContext`pm[ Pattern[$CellContext`n, Blank[]]] := Flatten[ Outer[List, Apply[Sequence, Table[{-1, 1}, {$CellContext`n}]]], $CellContext`n - 1], $CellContext`inv[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := If[$CellContext`plDims == 3, Translate[ Scale[{ PolyhedronData["Dodecahedron", "Faces"]}, {1, 1, 1} ($CellContext`scale/2), {0, 0, 0}], $CellContext`coords], $CellContext`poly2D[ 5, $CellContext`coords, $CellContext`scale]], $CellContext`poly2D[ Pattern[$CellContext`sides, Blank[]], Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]]] := Polygon[ Table[{Part[$CellContext`coords, 1] + $CellContext`scale Cos[2 Pi ($CellContext`i/$CellContext`sides)], Part[$CellContext`coords, 2] + $CellContext`scale Sin[2 Pi ($CellContext`i/$CellContext`sides)]}, \ {$CellContext`i, (-1)/2, $CellContext`sides - 1/2}]], $CellContext`utr[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := $CellContext`polyTri[$CellContext`coords, \ $CellContext`scale, Plus, "Icosahedron", $CellContext`plDims], $CellContext`dia[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := If[$CellContext`plDims == 3, Translate[ Scale[{ PolyhedronData["Octahedron", "Faces"]}, {1, 1, 1} $CellContext`scale, {0, 0, 0}], $CellContext`coords], Polygon[{{Part[$CellContext`coords, 1] - $CellContext`scale, Part[$CellContext`coords, 2]}, { Part[$CellContext`coords, 1], Part[$CellContext`coords, 2] + $CellContext`scale Sqrt[2]}, { Part[$CellContext`coords, 1] + $CellContext`scale, Part[$CellContext`coords, 2]}, { Part[$CellContext`coords, 1], Part[$CellContext`coords, 2] - $CellContext`scale Sqrt[3]}}]], $CellContext`squ[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := If[$CellContext`plDims == 3, Translate[ Scale[{ PolyhedronData["Cube", "Faces"]}, {1, 1, 1} $CellContext`scale, {0, 0, 0}], $CellContext`coords], $CellContext`poly2D[ 4, $CellContext`coords, $CellContext`scale]], $CellContext`cir[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := If[$CellContext`plDims == 3, Sphere[$CellContext`coords, $CellContext`scale], Disk[ Part[$CellContext`coords, Span[1, 2]], $CellContext`scale]], $CellContext`sets = 0, Attributes[Underscript] = {NHoldRest}, Pattern[$CellContext`flavorPattern, Underscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`fl]] := Flatten[{ Overscript[$CellContext`prt, Blank[]], $CellContext`prt}], Pattern[$CellContext`antiWhitePattern, Underscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`w]] := $CellContext`pAnti[ Underoverscript[$CellContext`prt, $CellContext`y, Blank[]]], Pattern[$CellContext`antiRedPattern, Underscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`r]] := $CellContext`pAnti[ Underoverscript[$CellContext`prt, $CellContext`bg, Blank[]]], Pattern[$CellContext`antiGreenPattern, Underscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`g]] := $CellContext`pAnti[ Underoverscript[$CellContext`prt, $CellContext`rb, Blank[]]], Pattern[$CellContext`antiBluePattern, Underscript[ Pattern[$CellContext`prt, Blank[]], $CellContext`b]] := $CellContext`pAnti[ Underoverscript[$CellContext`prt, $CellContext`rg, Blank[]]], Pattern[$CellContext`antiExPattern, Underscript[ Pattern[$CellContext`prt, Blank[]], "\" \""]] := $CellContext`pAnti[ Underoverscript[$CellContext`prt, $CellContext`rgb, Blank[]]], $CellContext`pAnti[ Pattern[$CellContext`p, Blank[]]] := $CellContext`position[$CellContext`e8Orig, - Part[$CellContext`e8Orig, Min[$CellContext`p, 256]]], $CellContext`flavorList = {{{$CellContext`e, \ $CellContext`\[Mu], $CellContext`\[Tau]}, { Subscript[$CellContext`\[Nu], $CellContext`e], Subscript[$CellContext`\[Nu], $CellContext`\[Mu]], Subscript[$CellContext`\[Nu], $CellContext`\[Tau]]}}, \ {{$CellContext`d, $CellContext`s, $CellContext`b}, {$CellContext`u, \ $CellContext`c, $CellContext`t}}, {{ Superscript[$CellContext`g, Row[{$CellContext`g, Overscript[$CellContext`b, Blank[]]}]], Superscript[$CellContext`g, Row[{$CellContext`r, Overscript[$CellContext`b, Blank[]]}]], Superscript[$CellContext`g, Row[{$CellContext`r, Overscript[$CellContext`g, Blank[]]}]]}, { Subscript[$CellContext`\[Omega], $CellContext`L], Subscript[$CellContext`\[Omega], $CellContext`R], \ $CellContext`W}}, {{ Row[{ Subscript[$CellContext`x, 1], $CellContext`\[CapitalPhi]}], Row[{ Subscript[$CellContext`x, 2], $CellContext`\[CapitalPhi]}], Row[{ Subscript[$CellContext`x, 3], $CellContext`\[CapitalPhi]}]}, { Row[{ Subscript[$CellContext`e, $CellContext`S], \ $CellContext`\[Phi]}], Row[{ Subscript[$CellContext`e, $CellContext`T], \ $CellContext`\[Phi]}], $CellContext`B}}, {{ Subscript[$CellContext`Ex, 1]}, { Subscript[$CellContext`Ex, 2]}}}, $CellContext`flavorListStr = {{{"e", "\[Mu]", "\[Tau]"}, { Subscript["\[Nu]", "e"], Subscript["\[Nu]", "\[Mu]"], Subscript["\[Nu]", "\[Tau]"]}}, {{"d", "s", "b"}, { "u", "c", "t"}}, {{ Superscript["g", Row[{"g", Overscript["b", "_"]}]], Superscript["g", Row[{"r", Overscript["b", "_"]}]], Superscript["g", Row[{"r", Overscript["g", "_"]}]]}, { Subscript["\[Omega]", "L"], Subscript["\[Omega]", "R"], "W"}}, {{ Row[{ Subscript["x", "1"], "\[CapitalPhi]"}], Row[{ Subscript["x", "2"], "\[CapitalPhi]"}], Row[{ Subscript["x", "3"], "\[CapitalPhi]"}]}, { Row[{ Subscript["e", "S"], "\[CapitalPhi]"}], Row[{ Subscript["e", "T"], "\[CapitalPhi]"}], "B"}}, {{ Subscript["Ex", "1"]}, { Subscript["Ex", "2"]}}}, $CellContext`qConvDoNoAnti = { "BottomQuark" -> "b", "BottomQuarkBar" -> "b", "CharmQuark" -> "c", "CharmQuarkBar" -> "c", "DownQuark" -> "d", "DownQuarkBar" -> "d", "StrangeQuark" -> "s", "StrangeQuarkBar" -> "s", "TopQuark" -> "t", "TopQuarkBar" -> "t", "UpQuark" -> "u", "UpQuarkBar" -> "u"}, $CellContext`colorListExp = {$CellContext`y, $CellContext`o, \ $CellContext`c, $CellContext`m, $CellContext`w, $CellContext`r, \ $CellContext`g, $CellContext`b, $CellContext`e, $CellContext`k}, \ $CellContext`colorList = { "y", "o", "c", "m", "w", "r", "g", "b", "e", "k"}, $CellContext`spList = { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}, $CellContext`fanoMult[ Pattern[$CellContext`perm, Blank[]], Pattern[$CellContext`triads, Blank[]], Pattern[$CellContext`sign, Blank[]]] := ($CellContext`fMult = Array[8& , {8, 8}]; $CellContext`fSign = 1 - 2 IdentityMatrix[8]; Map[(Part[$CellContext`fMult, 8, #] = ( Part[$CellContext`fMult, #, 8] = #); Part[$CellContext`fSign, 8, #] = (Part[$CellContext`fSign, #, 8] = 1))& , Range[8]]; Do[$CellContext`sgn = If[BitAnd[$CellContext`sign, 2^($CellContext`i - 1)] != 0, 1, -1]; Part[$CellContext`fMult, Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j - 1, 3]]], Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j + 0, 3]]]] = Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j + 1, 3]]]; Part[$CellContext`fSign, Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j - 1, 3]]], Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j + 0, 3]]]] = $CellContext`sgn; Part[$CellContext`fMult, Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j + 0, 3]]], Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j - 1, 3]]]] = Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j + 1, 3]]]; Part[$CellContext`fSign, Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j + 0, 3]]], Part[$CellContext`perm, Part[$CellContext`triads, $CellContext`i, 1 + Mod[$CellContext`j - 1, 3]]]] = -$CellContext`sgn, {$CellContext`i, 7}, {$CellContext`j, 3}]; {$CellContext`fMult, $CellContext`fSign}), $CellContext`j = 4, $CellContext`getTriads[ Pattern[$CellContext`invMask, Blank[]], Pattern[$CellContext`altMask, Blank[]], Pattern[$CellContext`fPi, Blank[]], Pattern[$CellContext`sm, Blank[]]] := Module[{$CellContext`c, $CellContext`d, $CellContext`e, \ $CellContext`triads, $CellContext`flatFanoStyled, $CellContext`flatFano, \ $CellContext`firstFlipSign}, $CellContext`flatFanoStyled = \ ($CellContext`flatFano = Join[ Drop[ Drop[ Take[ Flatten[$CellContext`triads = Map[($CellContext`c = Part[$CellContext`fano30Triads, $CellContext`fPi, #]; If[Part[ $CellContext`binMask[$CellContext`invMask, \ $CellContext`altMask, $CellContext`fPi, $CellContext`sm], #] == 1, Part[$CellContext`c, Span[2, All]] = RotateRight[ Rest[$CellContext`c]]]; $CellContext`c)& , Range[7]]], 9], {7}], {4}], {8}]); Map[If[ Or[ And[ MemberQ[ Part[#, If[$CellContext`fPi == $CellContext`flipSwitch, 3, 2]], $CellContext`fPi], $CellContext`invMask == \ $CellContext`altMask], And[ MemberQ[ Part[#, If[$CellContext`fPi == $CellContext`flipSwitch, 2, 3]], $CellContext`fPi], $CellContext`invMask != \ $CellContext`altMask]], $CellContext`d = \ $CellContext`position[$CellContext`flatFano, Part[#, 1, 1]]; $CellContext`e = \ $CellContext`position[$CellContext`flatFano, Part[#, 1, 2]]; Part[$CellContext`flatFanoStyled, $CellContext`d] = Style[ Part[#, 1, 2], $CellContext`pairClr[$CellContext`fPi], Bold]; Part[$CellContext`flatFanoStyled, $CellContext`e] = Style[ Part[#, 1, 1], $CellContext`pairClr[$CellContext`fPi], Bold]; Part[$CellContext`flatFano, $CellContext`d] = Part[#, 1, 2]; Part[$CellContext`flatFano, $CellContext`e] = Part[#, 1, 1]]& , $CellContext`flipFano]; $CellContext`firstFlipSign = If[First[$CellContext`triads] == Part[$CellContext`flatFano, Span[1, 3]], -1, 1]; {$CellContext`triads, $CellContext`flatFanoStyled, \ $CellContext`flatFano, $CellContext`firstFlipSign}], \ $CellContext`fano30Triads = CompressedData[" 1:eJxNkNuNAzEMA9eWSHUR4Fq6EtJA+v+Lno4/DCyIEWelv/fn/y3P87z8mb/4 XluWYtG2csNETcArtA2KUmAZcsFDbN5khUVCWKQtcMgzXmGJitQlKZK2a3Se sO2KIlMkbR+ywrZrd6aoyTNeYduTxBJte6xTnSeMm/iOOY4Q+Y6i0fkjK0xS ge40v8mQZ7zCFDXJENVGHrI6Txh3jvEm0XbcJMYOX3M6XYQmf+MVpqhJS1Fe yX8+Ou+QaTdtEr0RbhKzkdttOjl2XuMcO4v8Aq8pC6o= "], $CellContext`binMask[ Pattern[$CellContext`invMask, Blank[]], Pattern[$CellContext`altMask, Blank[]], Pattern[$CellContext`fPi, Blank[]], Pattern[$CellContext`sm, Blank[]]] := Reverse[ IntegerDigits[ FromDigits[ $CellContext`hexMask[$CellContext`invMask, $CellContext`altMask, \ $CellContext`fPi, $CellContext`sm], 16], 2, 7]], $CellContext`hexMask[ Pattern[$CellContext`invMask, Blank[]], Pattern[$CellContext`altMask, Blank[]], Pattern[$CellContext`fPi, Blank[]], Pattern[$CellContext`sm, Blank[]]] := Part[ If[$CellContext`invMask, $CellContext`fanoInv, \ $CellContext`fano240], $CellContext`fPi, Part[ $CellContext`smCnv[$CellContext`altMask], $CellContext`sm]], \ $CellContext`fanoInv = {{"77", "70", "6E", "69", "5D", "5A", "44", "43"}, { "74", "73", "6D", "6A", "5E", "59", "47", "40"}, { "7C", "7B", "65", "62", "56", "51", "4F", "48"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "75", "72", "6C", "6B", "5F", "58", "46", "41"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "7E", "79", "67", "60", "54", "53", "4D", "4A"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}, { "77", "70", "6E", "69", "5D", "5A", "44", "43"}, { "7F", "78", "66", "61", "55", "52", "4C", "4B"}, { "7C", "7B", "65", "62", "56", "51", "4F", "48"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}, { "75", "72", "6C", "6B", "5F", "58", "46", "41"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "74", "73", "6D", "6A", "5E", "59", "47", "40"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "7F", "78", "66", "61", "55", "52", "4C", "4B"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}, { "7E", "79", "67", "60", "54", "53", "4D", "4A"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "77", "70", "6E", "69", "5D", "5A", "44", "43"}, { "74", "73", "6D", "6A", "5E", "59", "47", "40"}, { "7C", "7B", "65", "62", "56", "51", "4F", "48"}, { "7D", "7A", "64", "63", "57", "50", "4E", "49"}, { "75", "72", "6C", "6B", "5F", "58", "46", "41"}, { "76", "71", "6F", "68", "5C", "5B", "45", "42"}}, $CellContext`fano240 = {{ "08", "0F", "11", "16", "22", "25", "3B", "3C"}, { "0B", "0C", "12", "15", "21", "26", "38", "3F"}, { "03", "04", "1A", "1D", "29", "2E", "30", "37"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "0A", "0D", "13", "14", "20", "27", "39", "3E"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "01", "06", "18", "1F", "2B", "2C", "32", "35"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}, { "08", "0F", "11", "16", "22", "25", "3B", "3C"}, { "00", "07", "19", "1E", "2A", "2D", "33", "34"}, { "03", "04", "1A", "1D", "29", "2E", "30", "37"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}, { "0A", "0D", "13", "14", "20", "27", "39", "3E"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "0B", "0C", "12", "15", "21", "26", "38", "3F"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "00", "07", "19", "1E", "2A", "2D", "33", "34"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}, { "01", "06", "18", "1F", "2B", "2C", "32", "35"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "08", "0F", "11", "16", "22", "25", "3B", "3C"}, { "0B", "0C", "12", "15", "21", "26", "38", "3F"}, { "03", "04", "1A", "1D", "29", "2E", "30", "37"}, { "02", "05", "1B", "1C", "28", "2F", "31", "36"}, { "0A", "0D", "13", "14", "20", "27", "39", "3E"}, { "09", "0E", "10", "17", "23", "24", "3A", "3D"}}, $CellContext`smCnv[ Pattern[$CellContext`altMask, Blank[]]] := If[$CellContext`altMask, $CellContext`leftSM, $CellContext`rightSM], \ $CellContext`leftSM = {2, 3, 5, 8}, $CellContext`rightSM = {1, 4, 6, 7}, $CellContext`flipSwitch = 28, $CellContext`pairClr[ Pattern[$CellContext`fPi, Blank[]]] := If[ MemberQ[ Flatten[$CellContext`c8Pairs], $CellContext`fPi], Blue, Red], $CellContext`c8Pairs = {{3, 5}, {6, 9}, {11, 12}, {13, 14}, { 18, 20}, {21, 22}, {27, 29}, { 30}}, $CellContext`flipFano = {{{2, 3}, {1, 3, 6, 4}, {2, 5}}, {{2, 4}, {8, 11}, {9, 7, 10, 12}}, {{2, 5}, {14, 16, 17, 18}, {13, 15}}, {{2, 6}, {22, 24}, {19, 20, 21, 23}}, {{2, 7}, {25, 27, 30}, {26, 29, 28}}}, $CellContext`localize = True, $CellContext`addParticles[ Pattern[$CellContext`p$, Blank[]]] := ( Map[{Part[$CellContext`dispArr$$, #] = "y"}& , $CellContext`p$]; If[$CellContext`localize, $CellContext`refresh$$ = True]), $CellContext`octIJKL := { I, $CellContext`\[DoubleStruckJ], $CellContext`\[DoubleStruckK], \ $CellContext`\[DoubleStruckL], I $CellContext`\[DoubleStruckL], $CellContext`\[DoubleStruckJ] \ $CellContext`\[DoubleStruckL], $CellContext`\[DoubleStruckK] $CellContext`\ \[DoubleStruckL], Subscript[$CellContext`\[ScriptE], 0]}, $CellContext`oct = { Subscript[$CellContext`\[ScriptE], 1], Subscript[$CellContext`\[ScriptE], 2], Subscript[$CellContext`\[ScriptE], 3], Subscript[$CellContext`\[ScriptE], 4], Subscript[$CellContext`\[ScriptE], 5], Subscript[$CellContext`\[ScriptE], 6], Subscript[$CellContext`\[ScriptE], 7], Subscript[$CellContext`\[ScriptE], 0]}, $CellContext`pmOctIJKL := Join[-$CellContext`octIJKL, $CellContext`octIJKL, {-1, 0, 1}], $CellContext`pmOct = {- Subscript[$CellContext`\[ScriptE], 1], - Subscript[$CellContext`\[ScriptE], 2], - Subscript[$CellContext`\[ScriptE], 3], - Subscript[$CellContext`\[ScriptE], 4], - Subscript[$CellContext`\[ScriptE], 5], - Subscript[$CellContext`\[ScriptE], 6], - Subscript[$CellContext`\[ScriptE], 7], - Subscript[$CellContext`\[ScriptE], 0], Subscript[$CellContext`\[ScriptE], 1], Subscript[$CellContext`\[ScriptE], 2], Subscript[$CellContext`\[ScriptE], 3], Subscript[$CellContext`\[ScriptE], 4], Subscript[$CellContext`\[ScriptE], 5], Subscript[$CellContext`\[ScriptE], 6], Subscript[$CellContext`\[ScriptE], 7], Subscript[$CellContext`\[ScriptE], 0], -1, 0, 1}, $CellContext`f[ Pattern[$CellContext`x, Blank[]]] := 3 $CellContext`x^2 ($CellContext`x - 1) ($CellContext`x + 1), $CellContext`a = 1, $CellContext`pTriad[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`flip, Blank[]]] := Module[{$CellContext`invMask, $CellContext`altMask, $CellContext`sm, \ $CellContext`fpC, $CellContext`fpG, $CellContext`d8Q, $CellContext`excFanoQ, \ $CellContext`genClr3Q, $CellContext`doD8, $CellContext`dropD8, \ $CellContext`fPi}, {$CellContext`invMask, $CellContext`altMask, \ $CellContext`sm, $CellContext`fpC, $CellContext`fpG} = \ $CellContext`getFPparam[$CellContext`p]; $CellContext`d8Q := \ $CellContext`invMask != $CellContext`altMask; $CellContext`doD8 := Or[ And[$CellContext`flip, $CellContext`d8Q], And[ Not[$CellContext`flip], Not[$CellContext`d8Q]]]; $CellContext`excFanoQ := And[$CellContext`fpC == 0, $CellContext`fpG == 0]; $CellContext`fPi := Part[ If[$CellContext`doD8, $CellContext`fpD8, $CellContext`fpC8], If[$CellContext`excFanoQ, 1, 0] + 2^2 $CellContext`fB[$CellContext`fpC, 2] + 2^2 $CellContext`fB[$CellContext`fpC, 1] + $CellContext`fB[$CellContext`fpG, 2] + $CellContext`fB[$CellContext`fpG, 1]]; {$CellContext`invMask, $CellContext`altMask, \ $CellContext`fPi, $CellContext`sm, $CellContext`fpC, $CellContext`fpG}], \ $CellContext`getFPparam[ Pattern[$CellContext`p, Blank[]]] := Condition[ Module[{$CellContext`invMask, $CellContext`altMask, \ $CellContext`sm, $CellContext`fpC, $CellContext`fpG}, $CellContext`invMask = If[$CellContext`aB[$CellContext`p] == 1, True, False]; $CellContext`altMask = If[$CellContext`pB[$CellContext`p] == If[$CellContext`ZLM, 1, 0], True, False]; $CellContext`sm = 1 + 2^1 $CellContext`s1B[$CellContext`p] + \ $CellContext`s0B[$CellContext`p]; $CellContext`fpC = 2^1 $CellContext`c1B[$CellContext`p] + \ $CellContext`c0B[$CellContext`p]; $CellContext`fpG = 2^1 $CellContext`g1B[$CellContext`p] + \ $CellContext`g0B[$CellContext`p]; {$CellContext`invMask, \ $CellContext`altMask, $CellContext`sm, $CellContext`fpC, $CellContext`fpG}], Not[$CellContext`swapQuat]], $CellContext`getFPparam[ Pattern[$CellContext`p, Blank[]]] := Condition[ Module[{$CellContext`invMask, $CellContext`altMask, \ $CellContext`sm, $CellContext`fpC, $CellContext`fpG}, $CellContext`invMask = If[$CellContext`g0B[$CellContext`p] == 1, True, False]; $CellContext`altMask = If[$CellContext`g1B[$CellContext`p] == If[$CellContext`ZLM, 1, 0], True, False]; $CellContext`sm = 1 + 2^1 $CellContext`c1B[$CellContext`p] + \ $CellContext`c0B[$CellContext`p]; $CellContext`fpC = 2^1 $CellContext`s1B[$CellContext`p] + \ $CellContext`s0B[$CellContext`p]; $CellContext`fpG = 2^1 $CellContext`pB[$CellContext`p] + \ $CellContext`aB[$CellContext`p]; {$CellContext`invMask, $CellContext`altMask, \ $CellContext`sm, $CellContext`fpC, $CellContext`fpG}], \ $CellContext`swapQuat], $CellContext`aB[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 1, 0], $CellContext`extBit[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`bOrdNum, Blank[]], Pattern[$CellContext`bOrdShift, Blank[]]] := $CellContext`fBit[ $CellContext`pBit[$CellContext`p], 2^(Part[$CellContext`bOrd, $CellContext`bOrdNum] + \ $CellContext`bOrdShift)], $CellContext`fBit[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`bit, Blank[]]] := $CellContext`fB[$CellContext`p, \ $CellContext`bit]/$CellContext`bit, $CellContext`pB[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 2, 0], $CellContext`ZLM = True, $CellContext`s1B[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 4, 1], $CellContext`s0B[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 4, 0], $CellContext`c1B[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 3, 1], $CellContext`c0B[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 3, 0], $CellContext`g1B[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 5, 1], $CellContext`g0B[ Pattern[$CellContext`p, Blank[]]] := $CellContext`extBit[$CellContext`p, 5, 0], $CellContext`swapQuat := False, $CellContext`pPhys[ Pattern[$CellContext`p, Blank[]]] := FullSimplify[ PowerExpand[ Dot[$CellContext`rot3, $CellContext`pE8[$CellContext`p]]]], $CellContext`rot3 = {{1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, { 0, 0, 1/Sqrt[2], -(1/Sqrt[2]), 0, 0, 0, 0}, { 0, 0, 1/Sqrt[2], 1/Sqrt[2], 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1/Sqrt[3], 1/Sqrt[3], 1/Sqrt[3]}, { 0, 0, 0, 0, 0, -(1/Sqrt[2]), 1/Sqrt[2], 0}, { 0, 0, 0, 0, 0, -(1/Sqrt[6]), -(1/Sqrt[6]), Sqrt[2/3]}}, $CellContext`pE8[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8Orig, Min[$CellContext`p, 256]], $CellContext`coords2 = {{ 1/4, Sqrt[3]/4}, {3/4, Sqrt[3]/4}, {1/2, 0}, { 1/2, 1/(2 Sqrt[3])}, {1, 0}, {1/2, Sqrt[3]/2}, {0, 0}, {1, 1}}, $CellContext`ca1 = {1, 2, 3}, $CellContext`coords3 = {{1, 0, 1}, {0, 1, 1}, {1, 1, 0}, {1, 1, 1}, {0, 1, 0}, {0, 0, 1}, {1, 0, 0}, {0, 0, 0}}, $CellContext`octString = { " \!\(\*SubscriptBox[\(\[ScriptE]\), \(1\)]\)\n =\[ImaginaryI] ", " \!\(\*SubscriptBox[\(\[ScriptE]\), \(2\)]\)\n =\[DoubleStruckJ] \ ", "\!\(\*SubscriptBox[\(\[ScriptE]\), \(3\)]\)=\[ImaginaryI]\[DoubleStruckJ]\ \n=\[DoubleStruckK]", " \!\(\*SubscriptBox[\(\[ScriptE]\), \(4\)]\)\n =\[DoubleStruckL] \ ", "\!\(\*SubscriptBox[\(\[ScriptE]\), \(5\)]\)\n=\[ImaginaryI]\ \[DoubleStruckL]", "\!\(\*SubscriptBox[\(\[ScriptE]\), \(6\)]\)\n=\[DoubleStruckJ]\ \[DoubleStruckL]", "\!\(\*SubscriptBox[\(\[ScriptE]\), \(7\)]\)=\[ImaginaryI]\ \[DoubleStruckJ]\[DoubleStruckL]\n=\[DoubleStruckK]\[DoubleStruckL]", "\!\(\*SubscriptBox[\(\[ScriptE]\), \(0\)]\)=1\n=\ \[DoubleStruckCapitalR]"}, $CellContext`imageSize = 643.75, $CellContext`pDisp[ Pattern[$CellContext`p$, Blank[]]] := Row[{"Ref. Symbols: 2D", Graphics[{ EdgeForm[Black], $CellContext`poly[ $CellContext`pShpSze[$CellContext`p$], {1, 1, 0}, 1/100., 2], { $CellContext`pColor[$CellContext`pGrad$$, $CellContext`pColr[$CellContext`p$], $CellContext`pShde[$CellContext`p$]], $CellContext`poly[ $CellContext`pShpSze[$CellContext`p$], {0, 0, 0}, 1/2, 2]}}, Background -> LightYellow, ImageSize -> 30], " 3D ", Graphics3D[{ $CellContext`poly[ $CellContext`pShpSze[$CellContext`p$], {1, 1, 1}, 1/100., 3], { $CellContext`pColor[$CellContext`pGrad$$, $CellContext`pColr[$CellContext`p$], $CellContext`pShde[$CellContext`p$]], $CellContext`poly[ $CellContext`pShpSze[$CellContext`p$], {0, 0, 0}, 1/2, 3]}}, Background -> LightYellow, ImageSize -> 50, Boxed -> False]}], $CellContext`poly[{ Pattern[$CellContext`type, Blank[]], Pattern[$CellContext`scaleFactor, Blank[]]}, Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := $CellContext`type[$CellContext`coords, \ $CellContext`scale $CellContext`scaleFactor, $CellContext`plDims], \ $CellContext`poly[ Subscript[ Pattern[$CellContext`type, Blank[]], Pattern[$CellContext`scaleFactor, Blank[]]], Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]], Pattern[$CellContext`plDims, Blank[]]] := $CellContext`poly[ ReleaseHold[ Subscript[$CellContext`type, $CellContext`scaleFactor]], \ $CellContext`coords, $CellContext`scale, $CellContext`plDims], \ $CellContext`pShpSze[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 5], $CellContext`pColor[ Pattern[$CellContext`grad, Blank[]], Pattern[$CellContext`color, Blank[]], Pattern[$CellContext`shade, Blank[]]] := If[$CellContext`color == "e", White, If[$CellContext`color == "k", Black, Part[ $CellContext`gradColors[$CellContext`grad], \ $CellContext`position[$CellContext`colorList, $CellContext`color] Length[$CellContext`shadeList] + 1 - $CellContext`position[$CellContext`shadeList, \ $CellContext`shade]]]], $CellContext`gradColors[ Pattern[$CellContext`grad, Blank[]]] := Switch[$CellContext`grad, 0, $CellContext`oldColors, 51, $CellContext`newColors, $CellContext`grad, Map[ColorData[ $CellContext`gradName[$CellContext`grad], #/ Length[$CellContext`newColors]]& , Range[ Length[$CellContext`newColors]]]], $CellContext`oldColors = { RGBColor[1, 1, 0.85], RGBColor[1, 1, 0], RGBColor[2/3, 2/3, 0], RGBColor[1, 0.9, 0.8], RGBColor[1, 0.5, 0], RGBColor[2/3, 0.33333333333333337`, 0], RGBColor[0.9, 1, 1], RGBColor[0, 1, 1], RGBColor[0, 2/3, 2/3], RGBColor[1, 0.9, 1], RGBColor[1, 0, 1], RGBColor[2/3, 0, 2/3], GrayLevel[0.85], GrayLevel[0.5], RGBColor[ 0.33333333333333337`, 0.33333333333333337`, 0.33333333333333337`], RGBColor[1, 0.85, 0.85], RGBColor[1, 0, 0], RGBColor[2/3, 0, 0], RGBColor[0.88, 1, 0.88], RGBColor[0, 1, 0], RGBColor[0, 2/3, 0], RGBColor[0.87, 0.94, 1], RGBColor[0, 0, 1], RGBColor[0, 0, 2/3]}, $CellContext`newColors = { RGBColor[{1, 1, 2/3}], RGBColor[{1, 1, 0}], RGBColor[{2/3, 2/3, 0}], RGBColor[{1, 0.9, 0.8}], RGBColor[{1, 1/2, 0}], RGBColor[{2/3, 1/3, 0}], RGBColor[{0.9, 1, 1}], RGBColor[{0, 1, 1}], RGBColor[{0, 2/3, 2/3}], RGBColor[{1, 0.9, 1}], RGBColor[{1, 0, 1}], RGBColor[{2/3, 0, 2/3}], RGBColor[{0.85, 0.85, 0.85}], RGBColor[{1/2, 1/2, 1/2}], RGBColor[{1/3, 1/3, 1/3}], RGBColor[{1, 0.85, 0.85}], RGBColor[{1, 0, 0}], RGBColor[{2/3, 0, 0}], RGBColor[{0.88, 1, 0.88}], RGBColor[{0, 1, 0}], RGBColor[{0, 2/3, 0}], RGBColor[{0.87, 0.94, 1}], RGBColor[{0, 0, 1}], RGBColor[{0, 0, 2/3}]}, $CellContext`gradName[ Pattern[$CellContext`grad, Blank[]]] := Switch[$CellContext`grad, 0, "oldColors", 51, "newColors", $CellContext`grad, Part[ ColorData[ "Gradients"], $CellContext`grad]], $CellContext`shadeList = { "d", "m", "l"}, $CellContext`pColr[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 4, 1], $CellContext`pShde[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 4, 2], $CellContext`pToolTipTxt[ Pattern[$CellContext`p, Blank[]]] := Grid[{{"Ref. Label: ", $CellContext`pLbl[$CellContext`p]}, {"Exp. Mass: ", $CellContext`pMass[$CellContext`p]}, {"Th. Mass: ", $CellContext`mTh[$CellContext`p]}, {"Exp. Lifetime: ", $CellContext`pLife[$CellContext`p]}, { Row[{"Bitwise #: ", $CellContext`pBit[$CellContext`p]}], Column[{ Row[{ $CellContext`toBits[$CellContext`p]}], Row[{ StringJoin[$CellContext`bStr, "-Bits"]}]}, Frame -> True]}, { Row[{"Clifford/Pascal E8 #: ", $CellContext`p}], $CellContext`pE8[$CellContext`p]}, {"E8 Root", $CellContext`pAlgebra[$CellContext`p]}, {"E8 Weight", $CellContext`pWeight[$CellContext`p]}, {"E8 Height", $CellContext`pHeight[$CellContext`p]}, $CellContext`pDispOct[$CellContext`p], If[$CellContext`localize, {"", ""}, { Column[{"Bitwise NKS CA", $CellContext`doCA[ $CellContext`pBit[$CellContext`p]]}], Column[{"Clifford/Pascal E8 CA", $CellContext`doCA[$CellContext`p - 1]}]}]}], $CellContext`pLbl[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 3], $CellContext`pMass[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 7], $CellContext`mTh[ Pattern[$CellContext`p, Blank[]]] := If[$CellContext`localize, "n/a", $CellContext`Convert[ $CellContext`M[ If[$CellContext`ZLM, 1 + $CellContext`pB[$CellContext`p], 2 - $CellContext`pB[$CellContext`p]], 1 + 2 $CellContext`c1B[$CellContext`p] + \ $CellContext`c0B[$CellContext`p], 2 $CellContext`g1B[$CellContext`p] + \ $CellContext`g0B[$CellContext`p], 1 + 2 $CellContext`s1B[$CellContext`p] + \ $CellContext`s0B[$CellContext`p]], $CellContext`Mega \ $CellContext`eVperC2]/($CellContext`Mega $CellContext`eVperC2)], \ $CellContext`M[ Pattern[$CellContext`oP, Blank[]], Pattern[$CellContext`oC, Blank[]], Pattern[$CellContext`oGen, Blank[]], Pattern[$CellContext`oS, Blank[]]] := $CellContext`zeroMass, $CellContext`zeroMass = 1.*^-14 $CellContext`MassUnit, $CellContext`pLife[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 8], $CellContext`toBits[ Pattern[$CellContext`p, Blank[]]] := PaddedForm[ BaseForm[ $CellContext`pBit[$CellContext`p], 2], 8, NumberPadding -> {"0", "0"}], $CellContext`bStr = "0apccssgg", $CellContext`pAlgebra[ Pattern[$CellContext`p, Blank[]]] := Dot[ Inverse[ Transpose[$CellContext`srE8]], $CellContext`pE8[$CellContext`p]], $CellContext`srE8 = {{0, -1, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, -1}, {-1, 0, 1, 0, 0, 0, 0, 0}, {0, 0, -1, 1, 0, 0, 0, 0}, {0, 0, 0, -1, 1, 0, 0, 0}, {0, 0, 0, 0, -1, 1, 0, 0}, {(-1)/2, 1/2, (-1)/2, (-1)/2, (-1)/2, (-1)/2, 1/2, (-1)/ 2}}, $CellContext`pWeight[ Pattern[$CellContext`p, Blank[]]] := Dot[$CellContext`cmE8, $CellContext`pAlgebra[$CellContext`p]], $CellContext`cmE8 = {{0, 0, 0, 0, 0, -1, 2, 0}, {0, 0, 0, 0, -1, 2, -1, 0}, {0, 0, 0, -1, 2, -1, 0, 0}, {0, 0, -1, 2, -1, 0, 0, 0}, {-1, -1, 2, -1, 0, 0, 0, 0}, {2, 0, -1, 0, 0, 0, 0, -1}, {-1, 0, 0, 0, 0, 0, 0, 2}, {0, 2, -1, 0, 0, 0, 0, 0}}, $CellContext`pHeight[ Pattern[$CellContext`p, Blank[]]] := 1 + Abs[ Total[ $CellContext`pAlgebra[$CellContext`p]]], $CellContext`pDispOct[ Pattern[$CellContext`p, Blank[]]] := { Column[{" Flipped ", Row[ $CellContext`pDispTriad[$CellContext`p, True]]}, Center, ItemSize -> If[ And[ Not[$CellContext`localize], $CellContext`listOut], 47, 32]], Column[{" Not Flipped ", Row[ $CellContext`pDispTriad[$CellContext`p, False]]}, Center, ItemSize -> If[ And[ Not[$CellContext`localize], $CellContext`listOut], 47, 32]]}, $CellContext`pDispTriad[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`flip, Blank[]]] := Apply[$CellContext`dispTriad, $CellContext`pTriad[$CellContext`p, $CellContext`flip]], \ $CellContext`dispTriad[ Pattern[$CellContext`invMask, Blank[]], Pattern[$CellContext`altMask, Blank[]], Pattern[$CellContext`fPi, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`fpC, Blank[]], Pattern[$CellContext`fpG, Blank[]]] := Module[{$CellContext`triads, $CellContext`flatFanoStyled, \ $CellContext`flatFano, $CellContext`firstFlipSign}, If[ And[$CellContext`fpC == 0, $CellContext`fpG == 0], {$CellContext`excMsg, $CellContext`excMsg}, { Column[{ Row[{"Octonion triads Fano index=", $CellContext`fPi, $CellContext`smQ[ Part[$CellContext`maskList, $CellContext`fPi]], "fp_sm=", Part[$CellContext`maskList, $CellContext`fPi]}], \ {$CellContext`triads, $CellContext`flatFanoStyled, $CellContext`flatFano, \ $CellContext`firstFlipSign} = $CellContext`getTriads[$CellContext`invMask, \ $CellContext`altMask, $CellContext`fPi, $CellContext`sm]; $CellContext`triads, If[ MemberQ[$CellContext`hoffmanSingleton, $CellContext`fPi], "HoffmanSingleton (Yellow)", "Coxeter (Cyan)"]}, Center, ItemSize -> 31], Column[{"flat triad/mask bits", Most[$CellContext`flatFanoStyled], $CellContext`binMask[$CellContext`invMask, \ $CellContext`altMask, $CellContext`fPi, $CellContext`sm], ""}, Center, ItemSize -> 15]}]], $CellContext`excMsg = Style[ Column[{" Invalid octonion ", "", " Fano plane not defined! ", ""}], RGBColor[1, 0, 0], Bold], $CellContext`smQ[ Pattern[$CellContext`sm, Blank[]]] := If[ MemberQ[$CellContext`leftSM, $CellContext`sm], " \!\(\*\nStyleBox[\"L\",\nFontColor->RGBColor[1, 0, 0],\n\ Background->RGBColor[1, 1, 0]]\) ", " \!\(\*\nStyleBox[\"R\",\nFontColor->RGBColor[0, 0, 1],\n\ Background->RGBColor[1, 1, 0]]\) "], $CellContext`maskList = {5, 8, 4, 3, 7, 6, 3, 2, 6, 5, 1, 4, 6, 7, 3, 3, 8, 6, 3, 1, 6, 6, 2, 3, 5, 8, 4, 3, 7, 6}, $CellContext`hoffmanSingleton = {2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30}, $CellContext`listOut = True, $CellContext`doCA[ Pattern[$CellContext`p, Blank[]]] := Row[{ ArrayPlot[ CellularAutomaton[ Min[$CellContext`p, 255], {{1}, 0}, 20], ImageSize -> {75, 75}, ImagePadding -> 2]}], $CellContext`specularity = 32., $CellContext`ca2 = {{1, 2}, {1, 3}, {2, 3}, {8, 1}, {8, 2}, {8, 3}, {8, 5}, {8, 6}, {8, 7}}, $CellContext`txt[ Pattern[$CellContext`lbl, Blank[]], Pattern[$CellContext`loc, Blank[]]] := Text[ Style[$CellContext`lbl, 14, Black], $CellContext`loc], $CellContext`odd4Edges = {{1, 2, 3} -> {4, 5, 6}, {1, 2, 3} -> {4, 5, 7}, {1, 2, 3} -> {4, 6, 7}, { 1, 2, 3} -> {5, 6, 7}, {1, 2, 4} -> {3, 5, 6}, {1, 2, 4} -> {3, 5, 7}, {1, 2, 4} -> {3, 6, 7}, {1, 2, 4} -> {5, 6, 7}, {1, 2, 5} -> {3, 4, 6}, {1, 2, 5} -> {3, 4, 7}, {1, 2, 5} -> {3, 6, 7}, { 1, 2, 5} -> {4, 6, 7}, {1, 2, 6} -> {3, 4, 5}, {1, 2, 6} -> {3, 4, 7}, {1, 2, 6} -> {3, 5, 7}, {1, 2, 6} -> {4, 5, 7}, {1, 2, 7} -> {3, 4, 5}, {1, 2, 7} -> {3, 4, 6}, {1, 2, 7} -> {3, 5, 6}, { 1, 2, 7} -> {4, 5, 6}, {1, 3, 4} -> {2, 5, 6}, {1, 3, 4} -> {2, 5, 7}, {1, 3, 4} -> {2, 6, 7}, {1, 3, 4} -> {5, 6, 7}, {1, 3, 5} -> {2, 4, 6}, {1, 3, 5} -> {2, 4, 7}, {1, 3, 5} -> {2, 6, 7}, { 1, 3, 5} -> {4, 6, 7}, {1, 3, 6} -> {2, 4, 5}, {1, 3, 6} -> {2, 4, 7}, {1, 3, 6} -> {2, 5, 7}, {1, 3, 6} -> {4, 5, 7}, {1, 3, 7} -> {2, 4, 5}, {1, 3, 7} -> {2, 4, 6}, {1, 3, 7} -> {2, 5, 6}, { 1, 3, 7} -> {4, 5, 6}, {1, 4, 5} -> {2, 3, 6}, {1, 4, 5} -> {2, 3, 7}, {1, 4, 5} -> {2, 6, 7}, {1, 4, 5} -> {3, 6, 7}, {1, 4, 6} -> {2, 3, 5}, {1, 4, 6} -> {2, 3, 7}, {1, 4, 6} -> {2, 5, 7}, { 1, 4, 6} -> {3, 5, 7}, {1, 4, 7} -> {2, 3, 5}, {1, 4, 7} -> {2, 3, 6}, {1, 4, 7} -> {2, 5, 6}, {1, 4, 7} -> {3, 5, 6}, {1, 5, 6} -> {2, 3, 4}, {1, 5, 6} -> {2, 3, 7}, {1, 5, 6} -> {2, 4, 7}, { 1, 5, 6} -> {3, 4, 7}, {1, 5, 7} -> {2, 3, 4}, {1, 5, 7} -> {2, 3, 6}, {1, 5, 7} -> {2, 4, 6}, {1, 5, 7} -> {3, 4, 6}, {1, 6, 7} -> {2, 3, 4}, {1, 6, 7} -> {2, 3, 5}, {1, 6, 7} -> {2, 4, 5}, { 1, 6, 7} -> {3, 4, 5}, {2, 3, 4} -> {5, 6, 7}, {2, 3, 5} -> {4, 6, 7}, {2, 3, 6} -> {4, 5, 7}, {2, 3, 7} -> {4, 5, 6}, {2, 4, 5} -> {3, 6, 7}, {2, 4, 6} -> {3, 5, 7}, {2, 4, 7} -> {3, 5, 6}, { 2, 5, 6} -> {3, 4, 7}, {2, 5, 7} -> {3, 4, 6}, {2, 6, 7} -> {3, 4, 5}}, $CellContext`triple35Lst = {{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 2, 7}, {1, 3, 4}, {1, 3, 5}, {1, 3, 6}, {1, 3, 7}, {1, 4, 5}, {1, 4, 6}, {1, 4, 7}, {1, 5, 6}, {1, 5, 7}, {1, 6, 7}, {2, 3, 4}, {2, 3, 5}, {2, 3, 6}, {2, 3, 7}, {2, 4, 5}, {2, 4, 6}, {2, 4, 7}, {2, 5, 6}, {2, 5, 7}, {2, 6, 7}, {3, 4, 5}, {3, 4, 6}, {3, 4, 7}, {3, 5, 6}, {3, 5, 7}, {3, 6, 7}, {4, 5, 6}, {4, 5, 7}, {4, 6, 7}, {5, 6, 7}}, $CellContext`odd4Hamiltonian = {1, 32, 5, 26, 15, 20, 31, 3, 34, 17, 11, 30, 21, 9, 23, 28, 4, 33, 8, 22, 7, 25, 6, 24, 27, 14, 16, 13, 19, 10, 18, 12, 29, 2, 35}, $CellContext`align = Spacer[57], $CellContext`o1 = {1, 2, 3, 4, 5, 6, 7, 8}, $CellContext`o2 = {4., 3.5, 3., 2.5, 2., 1.5, 1., 0.5}, $CellContext`doDynkin := With[{$CellContext`local$ = $CellContext`localDynkin}, Module[$CellContext`local$, $CellContext`rangeInc = 8; $CellContext`viewerScale = 44 $CellContext`rangeInc; $CellContext`xR = \ $CellContext`rangeInc/2; $CellContext`yR = 8/$CellContext`rangeInc; $CellContext`maxRangeX = \ $CellContext`xR ($CellContext`viewerScale/$CellContext`rangeInc); \ $CellContext`maxRangeY = $CellContext`yR \ ($CellContext`viewerScale/$CellContext`rangeInc); $CellContext`setName[ Pattern[$CellContext`i, Blank[]], Pattern[$CellContext`rank, Blank[]]] := If[$CellContext`i == 1, "Parent", If[$CellContext`i == 2^$CellContext`rank - 1, "OmniTruncated", If[ Or[$CellContext`i == 2^$CellContext`rank, $CellContext`i == 0], "Snub", If[$CellContext`i > 2^8, "UnNamed", Part[$CellContext`dynkNames, $CellContext`i, 2]]]]]; $CellContext`doAlg[ Pattern[$CellContext`alg1$, Blank[]]] := ($CellContext`alg$$ = StringJoin[ ToString[$CellContext`alg1$], Switch[$CellContext`affine$$, 3, ToString[Overscript[ ToString[$CellContext`rank$$ - $CellContext`affine$$], "~"]^"+++", TraditionalForm], 2, ToString[Overscript[ ToString[$CellContext`rank$$ - $CellContext`affine$$], "~"]^"^", TraditionalForm], 1, ToString[ Overscript[ ToString[$CellContext`rank$$ - $CellContext`affine$$], "~"], TraditionalForm], 0, ToString[$CellContext`rank$$]]]; $CellContext`group$$ = Switch[$CellContext`alg1$, "A", StringJoin["SL(", ToString[$CellContext`rank$$ + 1], ")"], "B", StringJoin["SO(", ToString[2 $CellContext`rank$$ + 1], ")"], "C", StringJoin["Sp(", ToString[2 $CellContext`rank$$], ")"], "D", StringJoin["SO(", ToString[2 $CellContext`rank$$], ")"], "E", StringJoin["\[Superset] O(", ToString[2 $CellContext`rank$$], ")"], "F", StringJoin["\[Superset] O(", ToString[2 $CellContext`rank$$ + 1], ")"], "G", StringJoin["\[Superset] O(", ToString[$CellContext`rank$$ + 1], ")"], "H", StringJoin["\[Superset] SL(2,", ToString[$CellContext`rank$$ + 1], ")"], "CUBE", StringJoin["SO(", ToString[2 $CellContext`rank$$ + 1], ")"], "?", "?"]); $CellContext`dynkRange[ Pattern[$CellContext`trim$, Blank[]]] := Range[ Min[ Length[$CellContext`dynkin$$] - $CellContext`affine$$ - Abs[$CellContext`trim$], Length[$CellContext`dynkin$$]]] + If[ And[$CellContext`trim$ > 0, Length[$CellContext`dynkin$$] - $CellContext`affine$$ - \ $CellContext`trim$ > 0], $CellContext`trim$, 0]; $CellContext`single[ Pattern[$CellContext`trim$, Blank[]]] := Or[Union[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[$CellContext`trim$], 2]] == {1}, Union[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[$CellContext`trim$], 2]] == {}]; $CellContext`linear[ Pattern[$CellContext`trim$, Blank[]]] := Max[ Map[Length[ Position[ Flatten[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[$CellContext`trim$], 1]], #]]& , Union[ Flatten[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[$CellContext`trim$], 1]]]]] < 3; $CellContext`arrow[ Pattern[$CellContext`coords, Blank[]], Pattern[$CellContext`scale, Blank[]]] := { Arrowheads[{{$CellContext`scale, 9/10}}], Arrow[$CellContext`coords]}; $CellContext`getNodeNear[ Pattern[$CellContext`ptNear$, Blank[]]] := $CellContext`position[ Part[$CellContext`ptsLoc$$, All, 1], $CellContext`ptNear$]; $CellContext`getLineNear[ Pattern[$CellContext`ptsNear$, Blank[]], Pattern[$CellContext`ptPos$, Blank[]]] := If[ MemberQ[ Part[$CellContext`dynkin$$, All, 1], {$CellContext`ptPos$, $CellContext`getNodeNear[ Part[$CellContext`ptsNear$, 2]]}], $CellContext`position[ Part[$CellContext`dynkin$$, All, 1], {$CellContext`ptPos$, $CellContext`getNodeNear[ Part[$CellContext`ptsNear$, 2]]}], If[ MemberQ[ Part[$CellContext`dynkin$$, All, 1], { $CellContext`getNodeNear[ Part[$CellContext`ptsNear$, 2]], $CellContext`ptPos$}], $CellContext`position[ Part[$CellContext`dynkin$$, All, 1], { $CellContext`getNodeNear[ Part[$CellContext`ptsNear$, 2]], $CellContext`ptPos$}], 1]]; $CellContext`addNode[ Pattern[$CellContext`ptPos$, Blank[]]] := Module[{$CellContext`addNewNode$, $CellContext`dropNodes$, \ $CellContext`addDropped$, $CellContext`drop$}, $CellContext`addNewNode$[ Pattern[$CellContext`p$, Blank[]]] := (AppendTo[$CellContext`ptsLoc$$, { Round[$CellContext`ptDD$$], 0}]; AppendTo[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1], { Round[$CellContext`ptDD$$], 0}]; $CellContext`addLine[{$CellContext`p$, Length[$CellContext`ptsLoc$$]}]); $CellContext`dropNodes$[ Pattern[$CellContext`dropNum$, Blank[]]] := ($CellContext`ptsLocSav$$ = Drop[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1], $CellContext`rank$$ - $CellContext`affine$$ - \ $CellContext`dropNum$]; $CellContext`dynkSav$$ = Drop[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2], Length[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2]] - $CellContext`affine$$ - $CellContext`dropNum$]; Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$]] = \ ({$CellContext`ptsLoc$$, $CellContext`dynkin$$, $CellContext`affine$$} = { Drop[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1], -$CellContext`affine$$ - $CellContext`dropNum$], Drop[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2], -$CellContext`affine$$ - $CellContext`dropNum$], \ $CellContext`affineTrk$$})); $CellContext`addDropped$[ Pattern[$CellContext`addNum$, Blank[]]] := Module[{$CellContext`i$, $CellContext`j$}, $CellContext`i$ = If[$CellContext`addNum$ > Length[$CellContext`ptsLocSav$$], $CellContext`addNum$ = Length[$CellContext`ptsLocSav$$]; 0, Length[$CellContext`ptsLocSav$$] - $CellContext`addNum$]; \ $CellContext`j$ = If[$CellContext`addNum$ > Length[$CellContext`dynkSav$$], $CellContext`addNum$ = Length[$CellContext`dynkSav$$]; 0, Length[$CellContext`dynkSav$$] - $CellContext`addNum$]; Map[AppendTo[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1], Part[$CellContext`ptsLocSav$$, 1 + $CellContext`addNum$ + $CellContext`i$ - #]]& , Range[$CellContext`addNum$]]; $CellContext`ptsLoc$$ = Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1]; Map[AppendTo[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2], {{ Part[$CellContext`dynkSav$$, #, 1, 1], 1 + Length[$CellContext`ptsLoc$$] - ($CellContext`j$ + \ $CellContext`addNum$)}, Part[$CellContext`dynkSav$$, #, 2]}]& , Range[$CellContext`addNum$]]; $CellContext`dynkin$$ = Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2]; If[ Or[$CellContext`i$ > 0, $CellContext`j$ > 0], $CellContext`ptsLocSav$$ = Drop[$CellContext`ptsLocSav$$, -$CellContext`i$]; \ $CellContext`dynkSav$$ = Drop[$CellContext`dynkSav$$, -$CellContext`j$]]]; \ $CellContext`drop$ = If[$CellContext`rank$$ - $CellContext`affine$$ - \ $CellContext`ptPos$ == 1, True, False]; If[ And[$CellContext`drop$, Or[$CellContext`patternD, $CellContext`patternE]], \ $CellContext`dropNodes$[ 1]; $CellContext`addNewNode$[$CellContext`ptPos$]; \ $CellContext`addDropped$[1], $CellContext`addNewNode$[$CellContext`ptPos$]]]; \ $CellContext`addLine[ Pattern[$CellContext`nodes$, Blank[]]] := ( AppendTo[$CellContext`dynkin$$, {$CellContext`nodes$, 1}]; AppendTo[ Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2], {$CellContext`nodes$, 1}]); $CellContext`doLine[ Pattern[$CellContext`k$, Blank[]], Pattern[$CellContext`delta$, Blank[]]] := Module[{$CellContext`x1$, $CellContext`y1$, $CellContext`x2$, \ $CellContext`y2$, $CellContext`angX$, $CellContext`angY$, \ $CellContext`newDelta$, $CellContext`theLine$, $CellContext`theArrow$}, \ $CellContext`x1$ = Part[$CellContext`ptsLoc$$, Part[$CellContext`dynkin$$, $CellContext`k$, 1, 1], 1, 1]; $CellContext`y1$ = Part[$CellContext`ptsLoc$$, Part[$CellContext`dynkin$$, $CellContext`k$, 1, 1], 1, 2]; $CellContext`x2$ = Part[$CellContext`ptsLoc$$, Part[$CellContext`dynkin$$, $CellContext`k$, 1, 2], 1, 1]; $CellContext`y2$ = Part[$CellContext`ptsLoc$$, Part[$CellContext`dynkin$$, $CellContext`k$, 1, 2], 1, 2]; $CellContext`angX$ = VectorAngle[{$CellContext`x2$, $CellContext`y2$} - \ {$CellContext`x1$, $CellContext`y1$}, {1, 0}]; $CellContext`angY$ = VectorAngle[{$CellContext`x2$, $CellContext`y2$} - \ {$CellContext`x1$, $CellContext`y1$}, {0, 1}]; $CellContext`newDelta$ = $CellContext`delta$ If[ Or[$CellContext`angX$ == Pi/4, $CellContext`angX$ == 3 (Pi/4)], {0, (3/2) Cos[$CellContext`angX$]}, { Sin[$CellContext`angX$], Cos[$CellContext`angX$]}]; $CellContext`theLine$ = \ {{$CellContext`x1$ + If[ Or[$CellContext`angX$ == 0, $CellContext`angX$ == Pi/4], 1/$CellContext`rangeInc - Abs[ Part[$CellContext`newDelta$, 2]], If[ Or[$CellContext`angX$ == Pi, $CellContext`angX$ == 3 (Pi/4)], (-1)/$CellContext`rangeInc + Abs[ Part[$CellContext`newDelta$, 2]], 0]], $CellContext`y1$ + If[ Or[ And[$CellContext`angX$ == Pi/2, $CellContext`angY$ != Pi], $CellContext`angX$ == $CellContext`angY$ == Pi/4, And[$CellContext`angX$ == 3 (Pi/4), $CellContext`angY$ == Pi/4]], 1/$CellContext`rangeInc - Abs[ Part[$CellContext`newDelta$, 2]], If[ Or[$CellContext`angY$ == Pi, $CellContext`angX$ == Pi/4, $CellContext`angX$ == 3 (Pi/4)], (-1)/$CellContext`rangeInc + Abs[ Part[$CellContext`newDelta$, 2]], 0]]} + $CellContext`newDelta$, {$CellContext`x2$ - If[ Or[$CellContext`angX$ == 0, $CellContext`angX$ == Pi/4], 1/$CellContext`rangeInc - Abs[ Part[$CellContext`newDelta$, 2]], If[ Or[$CellContext`angX$ == Pi, $CellContext`angX$ == 3 (Pi/4)], (-1)/$CellContext`rangeInc + Abs[ Part[$CellContext`newDelta$, 2]], 0]], $CellContext`y2$ - If[ Or[ And[$CellContext`angX$ == Pi/2, $CellContext`angY$ != Pi], $CellContext`angX$ == $CellContext`angY$ == Pi/4, And[$CellContext`angX$ == 3 (Pi/4), $CellContext`angY$ == Pi/4]], 1/$CellContext`rangeInc - Abs[ Part[$CellContext`newDelta$, 2]], If[ Or[$CellContext`angY$ == Pi, $CellContext`angX$ == Pi/4, $CellContext`angX$ == 3 (Pi/4)], (-1)/$CellContext`rangeInc + Abs[ Part[$CellContext`newDelta$, 2]], 0]]} + $CellContext`newDelta$}; $CellContext`theArrow$ = \ $CellContext`arrow[$CellContext`rangeInc {{$CellContext`x1$ + If[ Or[$CellContext`angX$ == 0, $CellContext`angX$ == Pi/4], Norm[{$CellContext`x2$ - $CellContext`x1$}]/2, If[ Or[$CellContext`angX$ == Pi, $CellContext`angX$ == 3 (Pi/4)], -Norm[{$CellContext`x2$ - $CellContext`x1$}]/2, 0]], $CellContext`y1$ + If[ Or[ And[$CellContext`angX$ == Pi/2, $CellContext`angY$ != Pi], $CellContext`angX$ == $CellContext`angY$ == Pi/4, And[$CellContext`angX$ == 3 (Pi/4), $CellContext`angY$ == Pi/4]], Norm[{$CellContext`y2$ - $CellContext`y1$}]/2, If[ Or[$CellContext`angY$ == Pi, $CellContext`angX$ == Pi/4, $CellContext`angX$ == 3 (Pi/4)], - Norm[{$CellContext`y2$ - $CellContext`y1$}]/2, 0]]}, {$CellContext`x2$, $CellContext`y2$}}, \ $CellContext`rangeInc/$CellContext`viewerScale]; {$CellContext`theLine$, \ $CellContext`theArrow$}]; $CellContext`doDDpane[ Pattern[$CellContext`j$, Blank[]], Pattern[$CellContext`rank$, Blank[]], Pattern[$CellContext`alg1$, Blank[]], Pattern[$CellContext`perm1$, Blank[]]] := Module[{$CellContext`delta$, $CellContext`theLine$, \ $CellContext`theArrow$, $CellContext`p$}, { Text[ Style[ Row[{ StringJoin[$CellContext`alg$$, " ", $CellContext`perm1$]}], Medium, Bold], $CellContext`rangeInc ( Part[$CellContext`ptsLoc$$, 1, 1] + {$CellContext`rank$/ If[$CellContext`affine$$ > 0, 4, 2], (-3)/4})], Map[{{ EdgeForm[{Thick, $CellContext`getColor[#]}], If[# > $CellContext`rank$ - $CellContext`affine$$, Black, If[Part[$CellContext`ptsLoc$$, #, 2] == 1, $CellContext`getColor[#], White]], Disk[$CellContext`rangeInc Part[$CellContext`ptsLoc$$, #, 1]]}, If[ Not[$CellContext`showPtext$$], Text[ Style[ ToString[# + 0], Small, Bold], $CellContext`rangeInc Part[$CellContext`ptsLoc$$, #, 1]], { Text[ Style[ ToString[# + 0], Small, Bold], $CellContext`rangeInc Part[$CellContext`ptsLoc$$, #, 1]], Text[ Style[ $CellContext`pLbl[$CellContext`p$ = \ $CellContext`position[$CellContext`algebra, ReplacePart[ Array[0& , 8], {# -> 1}]]], Small, Bold], $CellContext`rangeInc ({1, 1}/2 + Part[$CellContext`ptsLoc$$, #, 1])], Text[ Style[ StringJoin["3bit=", ToString[ FromDigits[{ $CellContext`extBit[$CellContext`p$, Part[$CellContext`bitOrd, Part[$CellContext`bitPerm, $CellContext`bP, 1]], 0], $CellContext`extBit[$CellContext`p$, Part[$CellContext`bitOrd, Part[$CellContext`bitPerm, $CellContext`bP, 2]], 0], $CellContext`extBit[$CellContext`p$, Part[$CellContext`bitOrd, Part[$CellContext`bitPerm, $CellContext`bP, 3]], 0]}, 2]]], Red, Small, Bold], $CellContext`rangeInc ({1/2, -1}/3 + Part[$CellContext`ptsLoc$$, #, 1])]}]}& , Range[ Length[$CellContext`ptsLoc$$]]], Map[{ Table[$CellContext`delta$ = If[ OddQ[$CellContext`i], Subtract, Plus][ 1/$CellContext`rangeInc, If[ Or[ Part[$CellContext`dynkin$$, #, 2] == 2, Part[$CellContext`dynkin$$, #, 2] == 5], If[$CellContext`i > 2, 1, -1], $CellContext`i/ 4]]/$CellContext`rangeInc; {$CellContext`theLine$, \ $CellContext`theArrow$} = $CellContext`doLine[#, $CellContext`delta$]; If[$CellContext`i == Part[$CellContext`dynkin$$, #, 2], Tooltip[{{ EdgeForm[Thick], $CellContext`getColor[#], Line[$CellContext`rangeInc $CellContext`theLine$]}}, Text[ Style[ ToString[{ Part[$CellContext`dynkin$$, #, 1, 1], Part[$CellContext`dynkin$$, #, 1, 2]} + 0], Medium, Bold]]], { EdgeForm[Thick], $CellContext`getColor[#], Line[$CellContext`rangeInc $CellContext`theLine$]}], \ {$CellContext`i, Part[$CellContext`dynkin$$, #, 2]}], If[ Or[$CellContext`alg1$ == "H", Part[$CellContext`dynkin$$, #, 2] == 1, Part[$CellContext`dynkin$$, #, 2] == 5], { PointSize[0], Opacity[1], White, Point[{0, 0}]}, $CellContext`theArrow$]}& , Range[ Length[$CellContext`dynkin$$]]]}]; $CellContext`getPerm := FromDigits[ Reverse[ Part[$CellContext`ptsLoc$$, All, 2]], 2]; $CellContext`lineCounts := Map[Length[ Position[ Flatten[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1]], #]]& , Union[ Flatten[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1]]]]; $CellContext`one3Line := And[Count[$CellContext`lineCounts, 3] == 1, Count[$CellContext`lineCounts, 1] == 3, Max[$CellContext`lineCounts] == 3]; $CellContext`patternA := And[ Or[ $CellContext`single[ 0], $CellContext`rank$$ - $CellContext`affine$$ == 1], Or[ $CellContext`linear[ 0], $CellContext`rank$$ - $CellContext`affine$$ < 4]]; $CellContext`patternB := And[ $CellContext`linear[0], $CellContext`single[-1], Part[ Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0]]], 2] == 2]; $CellContext`patternC := And[$CellContext`rank$$ - $CellContext`affine$$ > 2, $CellContext`linear[0], $CellContext`single[1], Part[ First[$CellContext`dynkin$$], 2] == 2]; $CellContext`patternD := And[ $CellContext`single[0], $CellContext`one3Line, Or[Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[-1], 1, 1]] == Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1, 1]], Part[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1, 1], 2] == Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1, 1]]]]; $CellContext`patternE := And[ $CellContext`single[ 0], $CellContext`one3Line, $CellContext`rank$$ - \ $CellContext`affine$$ > 5, Or[Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[-2], 1, 1]] == Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1, 1]], Part[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1, 1], 3] == Last[ Part[$CellContext`dynkin$$, $CellContext`dynkRange[0], 1, 1]]]]; $CellContext`patternF := And[ $CellContext`linear[ 0], $CellContext`rank$$ - $CellContext`affine$$ == 4, Part[$CellContext`dynkin$$, 1, 2] == 1, Part[$CellContext`dynkin$$, 2, 2] == 2, Part[$CellContext`dynkin$$, 3, 2] == 1]; $CellContext`patternG := And[$CellContext`rank$$ - $CellContext`affine$$ == 2, Part[$CellContext`dynkin$$, 1, 2] == 3]; $CellContext`patternH := And[ Or[$CellContext`rank$$ - $CellContext`affine$$ == 3, $CellContext`rank$$ - $CellContext`affine$$ == 4], $CellContext`linear[0], $CellContext`single[-1], Part[ Last[$CellContext`dynkin$$], 2] == 3]; $CellContext`patternCube := And[ $CellContext`linear[0], $CellContext`single[1], Part[ First[$CellContext`dynkin$$], 2] == 5]; $CellContext`setNodes := If[Length[$CellContext`ptsLoc$$] > 1, Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1, All, 2] = ( Part[$CellContext`ptsLoc$$, All, 2] = Reverse[ IntegerDigits[$CellContext`selDynkin$$, 2, Length[$CellContext`ptsLoc$$]]])]; $CellContext`clickEval := Module[{$CellContext`incNode$, $CellContext`incLine$, \ $CellContext`closeLoop$, $CellContext`checkNearNode$, $CellContext`ptsNear$, \ $CellContext`nrm$, $CellContext`ptPos$}, $CellContext`incNode$[ Pattern[$CellContext`ptPos$, Blank[]]] := (Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1, $CellContext`ptPos$, 2] = (Part[$CellContext`ptsLoc$$, $CellContext`ptPos$, 2] = Mod[Part[$CellContext`ptsLoc$$, $CellContext`ptPos$, 2] + 1, 2]); $CellContext`setPerm[$CellContext`rank$$]); \ $CellContext`incLine$[ Pattern[$CellContext`ptsNear$, Blank[]], Pattern[$CellContext`ptPos$, Blank[]]] := Module[{$CellContext`dynkPos$, $CellContext`curDynk$}, \ $CellContext`dynkPos$ = $CellContext`getLineNear[$CellContext`ptsNear$, \ $CellContext`ptPos$]; $CellContext`curDynk$ = Part[$CellContext`dynkin$$, $CellContext`dynkPos$, 2]; Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 2, $CellContext`dynkPos$, 2] = (Part[$CellContext`dynkin$$, $CellContext`dynkPos$, 2] = If[$CellContext`curDynk$ == 5, 1, PreIncrement[$CellContext`curDynk$]])]; \ $CellContext`closeLoop$[ Pattern[$CellContext`ptNear$, Blank[]], Pattern[$CellContext`ptPos$, Blank[]]] := ($CellContext`affineTrk$$ = 1; Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1, $CellContext`ptPos$, 2] = 0; $CellContext`addLine[{ $CellContext`getNodeNear[$CellContext`ptNear$], \ $CellContext`ptPos$}]); $CellContext`checkNearNode$[ Pattern[$CellContext`ptNear$, Blank[]], Pattern[$CellContext`ptPos$, Blank[]]] := If[ Not[ NumericQ[ Part[$CellContext`ptNear$, 1]]], False, And[ 0 < Norm[ Part[$CellContext`ptsLoc$$, $CellContext`ptPos$, 1] - $CellContext`ptNear$] < 2, Not[ MemberQ[ Part[$CellContext`dynkin$$, All, 1], {$CellContext`ptPos$, $CellContext`getNodeNear[$CellContext`ptNear$]}]], Not[ MemberQ[ Part[$CellContext`dynkin$$, All, 1], { $CellContext`getNodeNear[$CellContext`ptNear$], \ $CellContext`ptPos$}]]]]; $CellContext`ptsNear$ = Nearest[ Part[$CellContext`ptsLoc$$, All, 1], $CellContext`ptDD$$, 4]; $CellContext`nrm$ = Norm[$CellContext`ptDD$$ - Part[$CellContext`ptsNear$, 1]]; $CellContext`ptPos$ = $CellContext`getNodeNear[ Part[$CellContext`ptsNear$, 1]]; If[ Or[$CellContext`nrm$ < 1/$CellContext`rangeInc, And[$CellContext`nrm$ <= 1/Sqrt[2], If[$CellContext`rank$$ > 1, Norm[$CellContext`ptDD$$ - Part[$CellContext`ptsNear$, 2]] - $CellContext`nrm$ > 1/Sqrt[2], True]]], If[ And[Part[$CellContext`dynkTbl$$, Length[$CellContext`dynkTbl$$], 1, $CellContext`ptPos$, 2] == 1, Length[$CellContext`dynkin$$] > 1], If[ $CellContext`checkNearNode$[ Part[$CellContext`ptsNear$, 2], $CellContext`ptPos$], $CellContext`closeLoop$[ Part[$CellContext`ptsNear$, 2], $CellContext`ptPos$], If[ $CellContext`checkNearNode$[ Part[$CellContext`ptsNear$, 3], $CellContext`ptPos$], $CellContext`closeLoop$[ Part[$CellContext`ptsNear$, 3], $CellContext`ptPos$], If[Length[$CellContext`dynkin$$] > 2, If[ $CellContext`checkNearNode$[ Part[$CellContext`ptsNear$, 4], $CellContext`ptPos$], $CellContext`closeLoop$[ Part[$CellContext`ptsNear$, 4], $CellContext`ptPos$], $CellContext`incNode$[$CellContext`ptPos$]], $CellContext`incNode$[$CellContext`ptPos$]]]], $CellContext`incNode$[$CellContext`ptPos$]], If[ And[$CellContext`nrm$ <= 1/Sqrt[2], Norm[$CellContext`ptDD$$ - Part[$CellContext`ptsNear$, 2]] - $CellContext`nrm$ <= 1/Sqrt[2]], $CellContext`incLine$[$CellContext`ptsNear$, \ $CellContext`ptPos$], If[$CellContext`nrm$ <= 3/2, $CellContext`addNode[$CellContext`ptPos$], If[$CellContext`nrm$ > 3/2, $CellContext`ptsLoc$$ = {{ Round[$CellContext`ptDD$$], 1}}; $CellContext`dynkin$$ = {}; AppendTo[$CellContext`dynkTbl$$, {$CellContext`ptsLoc$$, \ $CellContext`dynkin$$, $CellContext`affine$$ = ($CellContext`affineTrk$$ = 0)}]; $CellContext`selDynkin$$ = 1]]]]; $CellContext`rank$$ = Length[$CellContext`ptsLoc$$]]; $CellContext`setPerm[ Pattern[$CellContext`rank$, Blank[]]] := Module[{$CellContext`i$}, $CellContext`selDynkin$$ = If[($CellContext`i$ = $CellContext`getPerm) == 0, $CellContext`rank$^2, $CellContext`i$]]; \ $CellContext`permname := ($CellContext`perm = \ $CellContext`setName[$CellContext`getPerm, $CellContext`rank$$]; If[$CellContext`permTrk$$ != $CellContext`perm, If[ NumericQ[$CellContext`rectification$$ = \ $CellContext`position[ Select[ Part[$CellContext`dynkNames, All, 2], StringMatchQ[#, StringExpression[ BlankNullSequence[], "Rectified"]]& ], $CellContext`perm]], \ $CellContext`refresh$$ = True, $CellContext`rectification$$ = 0]; $CellContext`permTrk$$ = $CellContext`perm]; \ $CellContext`perm); $CellContext`cartan := Module[{$CellContext`cm$ = 2 IdentityMatrix[$CellContext`rank$$]}, Map[($CellContext`cm$ = ReplacePart[ ReplacePart[$CellContext`cm$, Reverse[ Part[#, 1]] -> If[Part[#, 2] == 5, -2, -Part[#, 2]]], Part[#, 1] -> If[Part[#, 2] == 5, -2, -1]])& , $CellContext`dynkin$$]; $CellContext`cm$]; \ $CellContext`initDD := ($CellContext`selDynkinTrk$$ = \ ($CellContext`selDynkin$$ = 1); $CellContext`dynkTbl$$ = Part[$CellContext`dynkList, $CellContext`position[$CellContext`subGroups, ToLowerCase[$CellContext`selAlgebra$$]]]; \ {$CellContext`ptsLoc$$, $CellContext`dynkin$$, $CellContext`affine$$} = First[$CellContext`dynkTbl$$]; $CellContext`affineTrk$$ = \ $CellContext`affine$$; $CellContext`rank$$ = Length[$CellContext`ptsLoc$$]); $CellContext`initDynk := \ ($CellContext`algTrk$$ = "A1"; $CellContext`permTrk$$ = "Parent"; $CellContext`ptDDTrk$$ = ($CellContext`ptDD$$ = {0, 0}); $CellContext`selAlgebraTrk$$ = \ ($CellContext`selAlgebra$$ = First[ ToUpperCase[$CellContext`subGroups]]); $CellContext`initDD); If[$CellContext`init$$, $CellContext`initDynk; \ $CellContext`init$$ = False]; If[$CellContext`ptDDTrk$$ != $CellContext`ptDD$$, \ $CellContext`clickEval; $CellContext`ptDDTrk$$ = $CellContext`ptDD$$]; If[$CellContext`selAlgebraTrk$$ != $CellContext`selAlgebra$$, \ $CellContext`initDD; $CellContext`selAlgebraTrk$$ = \ $CellContext`selAlgebra$$]; If[$CellContext`selDynkinTrk$$ != $CellContext`selDynkin$$, \ $CellContext`setNodes; $CellContext`selDynkinTrk$$ = \ $CellContext`selDynkin$$]; Framed[ ClickPane[ Dynamic[ Graphics[{ Table[{$CellContext`ptsLoc$$, $CellContext`dynkin$$, \ $CellContext`affine$$} = Part[$CellContext`dynkTbl$$, $CellContext`j]; If[$CellContext`j == Length[$CellContext`dynkTbl$$], Part[$CellContext`dynkTbl$$, $CellContext`j, 3] = $CellContext`affineTrk$$; $CellContext`permName$$ = \ $CellContext`permname]; $CellContext`rank$$ = Length[$CellContext`ptsLoc$$]; \ $CellContext`doAlg[$CellContext`alg1$$ = Which[$CellContext`patternG, "G", $CellContext`patternF, "F", $CellContext`patternA, "A", $CellContext`patternCube, "CUBE", $CellContext`patternH, "H", $CellContext`patternE, "E", $CellContext`patternD, "D", $CellContext`patternC, "C", $CellContext`patternB, "B", True, "?"]]; If[$CellContext`algTrk$$ != $CellContext`alg$$, \ $CellContext`algTrk$$ = ($CellContext`lie$$ = $CellContext`alg$$)]; \ $CellContext`doDDpane[$CellContext`j, $CellContext`rank$$, \ $CellContext`alg1$$, $CellContext`setName[$CellContext`getPerm, \ $CellContext`rank$$]], {$CellContext`j, Length[$CellContext`dynkTbl$$]}], Text[ Style[ Column[{"Cartan Matrix:", $CellContext`cartan, Row[{"Group: ", $CellContext`group$$}]}], If[$CellContext`rank$$ > 11, Tiny, If[$CellContext`rank$$ > 8, Small, Medium]], Bold], If[$CellContext`rank$$ < 16, {(3.25 + 1/$CellContext`rank$$) $CellContext`xR, ( 33.75 + 1/$CellContext`rank$$) $CellContext`yR}, { 5 $CellContext`xR, 30 $CellContext`yR}]]}, ImageSize -> {$CellContext`xR $CellContext`viewerScale, \ $CellContext`yR $CellContext`viewerScale}, GridLines -> {$CellContext`rangeInc ( Range[1 + $CellContext`maxRangeX/$CellContext`rangeInc] - 1), $CellContext`rangeInc ( Range[1 + $CellContext`maxRangeY/$CellContext`rangeInc] - 1)}, AspectRatio -> $CellContext`yR/$CellContext`xR, GridLinesStyle -> Directive[Orange, Dashed, Opacity[1/8]], PlotRange -> {{1, $CellContext`maxRangeX}, { 1, $CellContext`maxRangeY}}]], ($CellContext`ptDD$$ = \ #/$CellContext`rangeInc)& ], Background -> None]]], $CellContext`localDynkin = {$CellContext`setName, \ $CellContext`setPerm, $CellContext`doAlg, $CellContext`dynkRange, \ $CellContext`single, $CellContext`linear, $CellContext`arrow, \ $CellContext`getNodeNear, $CellContext`getLineNear, $CellContext`addNode, \ $CellContext`addLine, $CellContext`doLine, $CellContext`doDDpane, \ $CellContext`permname, $CellContext`getPerm, $CellContext`lineCounts, \ $CellContext`one3Line, $CellContext`patternA, $CellContext`patternB, \ $CellContext`patternC, $CellContext`patternD, $CellContext`patternE, \ $CellContext`patternF, $CellContext`patternG, $CellContext`patternH, \ $CellContext`patternCube, $CellContext`setNodes, $CellContext`clickEval, \ $CellContext`cartan, $CellContext`initDD, $CellContext`initDynk}, \ $CellContext`rank$$ = 8, $CellContext`dynkNames = {{1, "Parent"}, {2, "Rectified"}, { 3, "Truncated"}, {4, "BiRectified"}, {5, "Cantellated"}, { 6, "BiTruncated"}, {7, "CantiTruncated"}, {8, "TriRectified"}, { 9, "Runcinated"}, {10, "BiCantellated"}, {11, "RunceTruncated"}, { 12, "TriTruncated"}, {13, "CantiRuncinated"}, { 14, "BiCantiTruncated"}, {15, "RunceCantiTruncated"}, { 16, "QuadriRectified"}, {17, "Stericated"}, {18, "BiRuncinated"}, { 19, "StereTruncated"}, {20, "TriCantellated"}, { 21, "RunceCantellated"}, {22, "BiRunceTruncated"}, { 23, "StereCantellated"}, {24, "QuadriTruncated"}, { 25, "RunceCantiCantellated"}, {26, "BiCantiRuncinated"}, { 27, "StereCantiCantellated"}, {28, "TriCantiTruncated"}, { 29, "RunciCantiStericated"}, {30, "BiRunceCantiTruncated"}, { 31, "SteriRunciCantiTruncated"}, {32, "QuintiRectified"}, { 33, "Pentellated"}, {34, "BiStericated"}, {35, "PenteTruncated"}, { 36, "TriRuncinated"}, {37, "CantiPentellated"}, { 38, "BiStereTruncated"}, {39, "RunceSteriRunciCantiTruncated"}, { 40, "QuadriCantellated"}, {41, "RunceRuncinated"}, { 42, "BiRunceCantellated"}, {43, "UnCalculated"}, { 44, "TriRunceTruncated"}, {45, "StereRuncinated"}, { 46, "BiStereCantellated"}, {47, "PenteRuncinated"}, { 48, "QuintiTruncated"}, {49, "StereCantiRuncinated"}, { 50, "BiRunceCantiCantellated"}, {51, "PenteCantiRuncinated"}, { 52, "TriCantiRuncinated"}, {53, "RunceRunciCantiRuncinated"}, { 54, "BiStereCantiCantellated"}, {55, "UnCalculated"}, { 56, "QuadriCantiTruncated"}, {57, "StereRunciCantiRuncinated"}, { 58, "BiRunciCantiStericated"}, {59, "PenteRunciCantiRuncinated"}, { 60, "TriRunceCantiTruncated"}, { 61, "SteriRunciCantiPentellated"}, { 62, "BiSteriRunciCantiTruncated"}, { 63, "PentiSteriRunciCantiTruncated"}, {64, "HexaRectified"}, { 65, "Hexicated"}, {66, "BiPentellated"}, {67, "HexeTruncated"}, { 68, "TriStericated"}, {69, "CantiHexicated"}, { 70, "BiPenteTruncated"}, { 71, "RuncePentiSteriRunciCantiTruncated"}, { 72, "QuadriRuncinated"}, {73, "StereSteriRunciCantiRuncinated"}, { 74, "BiCantiPentellated"}, { 75, "PenteSteriRunciCantiRuncinated"}, {76, "TriStereTruncated"}, { 77, "RunciCantiHexicated"}, { 78, "BiRunceSteriRunciCantiTruncated"}, {79, "UnCalculated"}, { 80, "QuintiCantellated"}, {81, "RunceStericated"}, { 82, "BiRunceRuncinated"}, { 83, "SterePentiSteriRunciCantiCantellated"}, { 84, "TriRunceCantellated"}, {85, "RunceCantiStericated"}, { 86, "UnCalculated"}, {87, "UnCalculated"}, { 88, "QuadriRunceTruncated"}, {89, "StereStericated"}, { 90, "BiStereRuncinated"}, {91, "UnCalculated"}, { 92, "TriStereCantellated"}, {93, "PenteStericated"}, { 94, "BiPenteRuncinated"}, {95, "HexeStericated"}, { 96, "HexaTruncated"}, {97, "PenteCantiStericated"}, { 98, "BiStereCantiRuncinated"}, {99, "HexeCantiStericated"}, { 100, "TriRunceCantiCantellated"}, { 101, "StereRunciCantiStericated"}, { 102, "BiPenteCantiRuncinated"}, {103, "UnCalculated"}, { 104, "QuadriCantiRuncinated"}, { 105, "PenteRunciCantiStericated"}, { 106, "BiRunceRunciCantiRuncinated"}, { 107, "HexeRunciCantiStericated"}, { 108, "TriStereCantiCantellated"}, { 109, "RunceSteriRunciCantiStericated"}, {110, "UnCalculated"}, { 111, "UnCalculated"}, {112, "QuintiCantiTruncated"}, { 113, "UnCalculated"}, {114, "BiStereRunciCantiRuncinated"}, { 115, "UnCalculated"}, {116, "TriRunciCantiStericated"}, { 117, "StereSteriRunciCantiStericated"}, { 118, "BiPenteRunciCantiRuncinated"}, {119, "UnCalculated"}, { 120, "QuadriRunceCantiTruncated"}, { 121, "PenteSteriRunciCantiStericated"}, { 122, "BiSteriRunciCantiPentellated"}, { 123, "HexeSteriRunciCantiStericated"}, { 124, "TriSteriRunciCantiTruncated"}, { 125, "PentiSteriRunciCantiHexicated"}, { 126, "BiPentiSteriRunciCantiTruncated"}, { 127, "HexiPentiSteriRunciCantiTruncated"}, { 128, "HeptaRectified"}, {129, "CantePentellated"}, { 130, "BiHexicated"}, {131, "HepteTruncated"}, { 132, "TriPentellated"}, {133, "CanteCantiPentellated"}, { 134, "BiHexeTruncated"}, { 135, "RunceHexiPentiSteriRunciCantiTruncated"}, { 136, "QuadriStericated"}, {137, "UnCalculated"}, { 138, "BiCantiHexicated"}, {139, "UnCalculated"}, { 140, "TriPenteTruncated"}, {141, "CanteRunciCantiPentellated"}, { 142, "BiRuncePentiSteriRunciCantiTruncated"}, { 143, "UnCalculated"}, {144, "QuintiRuncinated"}, { 145, "RunceHexiPentiSteriRunciCantiCantellated"}, { 146, "BiStereSteriRunciCantiRuncinated"}, { 147, "StereHexiPentiSteriRunciCantiCantellated"}, { 148, "TriCantiPentellated"}, { 149, "SterePentiSteriRunciCantiStericated"}, { 150, "BiPenteSteriRunciCantiRuncinated"}, {151, "UnCalculated"}, { 152, "QuadriStereTruncated"}, { 153, "PentePentiSteriRunciCantiStericated"}, { 154, "BiRunciCantiHexicated"}, { 155, "HexePentiSteriRunciCantiStericated"}, { 156, "TriRunceSteriRunciCantiTruncated"}, { 157, "CanteSteriRunciCantiPentellated"}, {158, "UnCalculated"}, { 159, "UnCalculated"}, {160, "HexaCantellated"}, { 161, "RuncePentellated"}, {162, "BiRunceStericated"}, { 163, "UnCalculated"}, {164, "TriRunceRuncinated"}, { 165, "RunceCantiPentellated"}, { 166, "BiSterePentiSteriRunciCantiCantellated"}, { 167, "UnCalculated"}, {168, "QuadriRunceCantellated"}, { 169, "StereHexiPentiSteriRunciCantiRuncinated"}, { 170, "BiRunceCantiStericated"}, { 171, "PenteHexiPentiSteriRunciCantiRuncinated"}, { 172, "HexeHexiPentiSteriRunciCantiRuncinated"}, { 173, "RunceRunciCantiPentellated"}, {174, "UnCalculated"}, { 175, "UnCalculated"}, {176, "QuintiRunceTruncated"}, { 177, "SterePentellated"}, {178, "BiStereStericated"}, { 179, "UnCalculated"}, {180, "TriStereRuncinated"}, { 181, "StereCantiPentellated"}, {182, "UnCalculated"}, { 183, "UnCalculated"}, {184, "QuadriStereCantellated"}, { 185, "PentePentellated"}, {186, "BiPenteStericated"}, { 187, "UnCalculated"}, {188, "TriPenteRuncinated"}, { 189, "HexePentellated"}, {190, "BiHexeStericated"}, { 191, "HeptePentellated"}, {192, "HeptaTruncated"}, { 193, "HexeCantiPentellated"}, {194, "BiPenteCantiStericated"}, { 195, "HepteCantiPentellated"}, {196, "TriStereCantiRuncinated"}, { 197, "PenteRunciCantiPentellated"}, { 198, "BiHexeCantiStericated"}, {199, "UnCalculated"}, { 200, "QuadriRunceCantiCantellated"}, { 201, "HexeRunciCantiPentellated"}, { 202, "BiStereRunciCantiStericated"}, { 203, "HepteRunciCantiPentellated"}, { 204, "TriPenteCantiRuncinated"}, { 205, "StereSteriRunciCantiPentellated"}, {206, "UnCalculated"}, { 207, "UnCalculated"}, {208, "QuintiCantiRuncinated"}, { 209, "UnCalculated"}, {210, "BiPenteRunciCantiStericated"}, { 211, "UnCalculated"}, {212, "TriRunceRunciCantiRuncinated"}, { 213, "PenteSteriRunciCantiPentellated"}, { 214, "BiHexeRunciCantiStericated"}, {215, "UnCalculated"}, { 216, "QuadriStereCantiCantellated"}, { 217, "HexeSteriRunciCantiPentellated"}, { 218, "BiRunceSteriRunciCantiStericated"}, { 219, "HepteSteriRunciCantiPentellated"}, { 220, "HepteHexiPentiSteriRunciCantiStericated"}, { 221, "RuncePentiSteriRunciCantiPentellated"}, { 222, "UnCalculated"}, {223, "UnCalculated"}, { 224, "HexaCantiTruncated"}, {225, "UnCalculated"}, { 226, "UnCalculated"}, {227, "UnCalculated"}, { 228, "TriStereRunciCantiRuncinated"}, {229, "UnCalculated"}, { 230, "UnCalculated"}, {231, "UnCalculated"}, { 232, "QuadriRunciCantiStericated"}, {233, "UnCalculated"}, { 234, "BiStereSteriRunciCantiStericated"}, {235, "UnCalculated"}, { 236, "TriPenteRunciCantiRuncinated"}, { 237, "SterePentiSteriRunciCantiPentellated"}, { 238, "UnCalculated"}, {239, "UnCalculated"}, { 240, "QuintiRunceCantiTruncated"}, {241, "UnCalculated"}, { 242, "BiPenteSteriRunciCantiStericated"}, {243, "UnCalculated"}, { 244, "TriSteriRunciCantiPentellated"}, { 245, "PentePentiSteriRunciCantiPentellated"}, { 246, "BiHexeSteriRunciCantiStericated"}, {247, "UnCalculated"}, { 248, "QuadriSteriRunciCantiTruncated"}, { 249, "HexePentiSteriRunciCantiPentellated"}, { 250, "BiPentiSteriRunciCantiHexicated"}, { 251, "HeptePentiSteriRunciCantiPentellated"}, { 252, "TriPentiSteriRunciCantiTruncated"}, { 253, "CanteHexiPentiSteriRunciCantiPentellated"}, { 254, "BiHexiPentiSteriRunciCantiTruncated"}, { 255, "OmniTruncated"}, {256, "Snub"}}, $CellContext`x1 = 28352, $CellContext`getColor[ Pattern[$CellContext`grad, Blank[]], Pattern[$CellContext`i, Blank[]]] := $CellContext`pColor[$CellContext`grad, Part[$CellContext`colorList, Mod[$CellContext`i - 1, Length[$CellContext`cList]] + 1], Part[$CellContext`shadeList, Length[$CellContext`shadeList] + 1 - Floor[Mod[$CellContext`i + Length[$CellContext`cList] - 1, Length[$CellContext`newColors]]/Length[$CellContext`cList] + 1]]], $CellContext`getColor[ Pattern[$CellContext`i$, Blank[]]] := $CellContext`getColor[$CellContext`pGrad$$, \ $CellContext`i$], $CellContext`cList = { "RGBColor[1, 1, 0]", "RGBColor[1, 0.5, 0]", "RGBColor[0, 1, 1]", "RGBColor[1, 0, 1]", "GrayLevel[0.5]", "RGBColor[1, 0, 0]", "RGBColor[0, 1, 0]", "RGBColor[0, 0, 1]"}, $CellContext`algebra = {{-3, -3, -5, -4, -3, \ -2, -1, -1}, {(-1)/2, (-1)/2, 0, 0, 0, 0, 0, 0}, {(-7)/2, (-5)/ 2, -5, -4, -3, -2, -1, -2}, {(-1)/2, (-1)/2, -1, -1, -1, -1, -1, 0}, {(-1)/2, (-1)/2, -1, -1, -1, -1, 0, 0}, {(-1)/2, (-1)/ 2, -1, -1, -1, 0, 0, 0}, {(-1)/2, (-1)/2, -1, -1, 0, 0, 0, 0}, { 1/2, (-1)/2, 0, 0, 0, 0, 0, 0}, {(-1)/2, (-1)/2, -1, 0, 0, 0, 0, 0}, {-3, -2, -4, -4, -3, -2, -1, -1}, {-2, -2, -3, -3, -3, -2, \ -1, -1}, {-2, -2, -3, -3, -2, -2, -1, -1}, {-2, -2, -3, -3, -2, -1, -1, -1}, \ {-2, -2, -3, -3, -2, -1, 0, -1}, {1, 0, 1, 0, 0, 0, 0, 1}, {-2, -2, -4, -4, -3, -2, -1, -1}, {-3, -2, -4, -3, -3, -2, -1, \ -1}, {-3, -2, -4, -3, -2, -2, -1, -1}, {-3, -2, -4, -3, -2, -1, -1, -1}, {-3, \ -2, -4, -3, -2, -1, 0, -1}, {0, 0, 0, 0, 0, 0, 0, 1}, {-3, -2, -5, -4, -3, -2, -1, -1}, {-2, -2, -3, -2, -2, -2, -1, \ -1}, {-2, -2, -3, -2, -2, -1, -1, -1}, {-2, -2, -3, -2, -2, -1, 0, -1}, {1, 0, 1, 1, 0, 0, 0, 1}, {-2, -2, -4, -3, -3, -2, -1, -1}, {-2, -2, -3, -2, -1, -1, -1, \ -1}, {-2, -2, -3, -2, -1, -1, 0, -1}, {1, 0, 1, 1, 1, 0, 0, 1}, {-2, -2, -4, -3, -2, -2, -1, -1}, {-2, -2, -3, -2, -1, 0, 0, -1}, {1, 0, 1, 1, 1, 1, 0, 1}, {-2, -2, -4, -3, -2, -1, -1, -1}, {1, 0, 1, 1, 1, 1, 1, 1}, {-2, -2, -4, -3, -2, -1, 0, -1}, {1, 0, 0, 0, 0, 0, 0, 1}, { 0, -1, -1, 0, 0, 0, 0, 0}, {-1, -1, -2, -1, 0, 0, 0, 0}, {-1, -1, -2, -1, -1, 0, 0, 0}, {-1, -1, -2, -1, -1, -1, 0, 0}, {-1, -1, -2, -1, -1, -1, -1, 0}, {-4, -3, -6, -4, -3, -2, -1, -2}, {-1, -1, -1, 0, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0, 0, 0}, {3, 2, 4, 4, 3, 2, 1, 2}, {0, 0, 0, 1, 1, 1, 1, 0}, {0, 0, 0, 1, 1, 1, 0, 0}, {0, 0, 0, 1, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {-1, 0, -1, 0, 0, 0, 0, 0}, { 0, -1, -1, -1, 0, 0, 0, 0}, {0, -1, -1, -1, -1, 0, 0, 0}, { 0, -1, -1, -1, -1, -1, 0, 0}, {0, -1, -1, -1, -1, -1, -1, 0}, {-3, -3, -5, -4, -3, -2, -1, -2}, {0, -1, 0, 0, 0, 0, 0, 0}, { 1, 0, 0, 0, 0, 0, 0, 0}, {4, 2, 5, 4, 3, 2, 1, 2}, {1, 0, 1, 1, 1, 1, 1, 0}, {1, 0, 1, 1, 1, 1, 0, 0}, {1, 0, 1, 1, 1, 0, 0, 0}, {1, 0, 1, 1, 0, 0, 0, 0}, {-1, -1, -2, -2, -1, 0, 0, 0}, {-1, -1, -2, -2, -1, -1, 0, 0}, {-1, -1, -2, -2, -1, -1, -1, 0}, {-4, -3, -6, -5, -3, -2, -1, -2}, {-1, -1, -1, -1, 0, 0, 0, 0}, {0, 0, -1, -1, 0, 0, 0, 0}, {3, 2, 4, 3, 3, 2, 1, 2}, {0, 0, 0, 0, 1, 1, 1, 0}, {0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {-1, -1, -2, -2, -2, -1, 0, 0}, {-1, -1, -2, -2, -2, -1, -1, 0}, {-4, -3, -6, -5, -4, -2, -1, -2}, {-1, -1, -1, -1, -1, 0, 0, 0}, {0, 0, -1, -1, -1, 0, 0, 0}, {3, 2, 4, 3, 2, 2, 1, 2}, {0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {-1, -1, -2, -2, -2, -2, -1, 0}, {-4, -3, -6, -5, -4, -3, -1, -2}, {-1, -1, -1, -1, -1, -1, 0, 0}, {0, 0, -1, -1, -1, -1, 0, 0}, {3, 2, 4, 3, 2, 1, 1, 2}, {0, 0, 0, 0, 0, 0, 1, 0}, {-4, -3, -6, -5, -4, -3, -2, -2}, {-1, -1, -1, -1, -1, -1, -1, 0}, {0, 0, -1, -1, -1, -1, -1, 0}, {3, 2, 4, 3, 2, 1, 0, 2}, {-4, -3, -5, -4, -3, -2, -1, -2}, {-3, -2, -5, -4, -3, -2, -1, \ -2}, {-2, -1, -2, -2, -2, -2, -1, -1}, {-2, -1, -2, -2, -2, -1, -1, -1}, {-2, \ -1, -2, -2, -2, -1, 0, -1}, {1, 1, 2, 1, 0, 0, 0, 1}, {-2, -1, -3, -3, -3, -2, -1, -1}, {-2, -1, -2, -2, -1, -1, -1, \ -1}, {-2, -1, -2, -2, -1, -1, 0, -1}, {1, 1, 2, 1, 1, 0, 0, 1}, {-2, -1, -3, -3, -2, -2, -1, -1}, {-2, -1, -2, -2, -1, 0, 0, -1}, {1, 1, 2, 1, 1, 1, 0, 1}, {-2, -1, -3, -3, -2, -1, -1, -1}, {1, 1, 2, 1, 1, 1, 1, 1}, {-2, -1, -3, -3, -2, -1, 0, -1}, {1, 1, 1, 0, 0, 0, 0, 1}, {-1, -1, -1, -1, -1, -1, -1, -1}, {-1, -1, -1, -1, -1, -1, 0, -1}, {2, 1, 3, 2, 1, 0, 0, 1}, {-1, -1, -2, -2, -2, -2, -1, -1}, {-1, -1, -1, -1, -1, 0, 0, -1}, {2, 1, 3, 2, 1, 1, 0, 1}, {-1, -1, -2, -2, -2, -1, -1, -1}, {2, 1, 3, 2, 1, 1, 1, 1}, {-1, -1, -2, -2, -2, -1, 0, -1}, {2, 1, 2, 1, 0, 0, 0, 1}, {-1, -1, -1, -1, 0, 0, 0, -1}, {2, 1, 3, 2, 2, 1, 0, 1}, {-1, -1, -2, -2, -1, -1, -1, -1}, {2, 1, 3, 2, 2, 1, 1, 1}, {-1, -1, -2, -2, -1, -1, 0, -1}, {2, 1, 2, 1, 1, 0, 0, 1}, {2, 1, 3, 2, 2, 2, 1, 1}, {-1, -1, -2, -2, -1, 0, 0, -1}, {2, 1, 2, 1, 1, 1, 0, 1}, {2, 1, 2, 1, 1, 1, 1, 1}, {-2, -1, -2, -1, -1, -1, -1, -1}, {-2, -1, -2, -1, -1, -1, 0, -1}, {1, 1, 2, 2, 1, 0, 0, 1}, {-2, -1, -3, -2, -2, -2, -1, -1}, {-2, -1, -2, -1, -1, 0, 0, -1}, {1, 1, 2, 2, 1, 1, 0, 1}, {-2, -1, -3, -2, -2, -1, -1, -1}, {1, 1, 2, 2, 1, 1, 1, 1}, {-2, -1, -3, -2, -2, -1, 0, -1}, {1, 1, 1, 1, 0, 0, 0, 1}, {-2, -1, -2, -1, 0, 0, 0, -1}, {1, 1, 2, 2, 2, 1, 0, 1}, {-2, -1, -3, -2, -1, -1, -1, -1}, {1, 1, 2, 2, 2, 1, 1, 1}, {-2, -1, -3, -2, -1, -1, 0, -1}, {1, 1, 1, 1, 1, 0, 0, 1}, {1, 1, 2, 2, 2, 2, 1, 1}, {-2, -1, -3, -2, -1, 0, 0, -1}, {1, 1, 1, 1, 1, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1}, {-1, -1, -1, 0, 0, 0, 0, -1}, {2, 1, 3, 3, 2, 1, 0, 1}, {-1, -1, -2, -1, -1, -1, -1, -1}, {2, 1, 3, 3, 2, 1, 1, 1}, {-1, -1, -2, -1, -1, -1, 0, -1}, {2, 1, 2, 2, 1, 0, 0, 1}, {2, 1, 3, 3, 2, 2, 1, 1}, {-1, -1, -2, -1, -1, 0, 0, -1}, {2, 1, 2, 2, 1, 1, 0, 1}, {2, 1, 2, 2, 1, 1, 1, 1}, {2, 1, 3, 3, 3, 2, 1, 1}, {-1, -1, -2, -1, 0, 0, 0, -1}, {2, 1, 2, 2, 2, 1, 0, 1}, {2, 1, 2, 2, 2, 1, 1, 1}, {2, 1, 2, 2, 2, 2, 1, 1}, {3, 2, 5, 4, 3, 2, 1, 2}, {4, 3, 5, 4, 3, 2, 1, 2}, {-3, -2, -4, -3, -2, -1, 0, -2}, {0, 0, 1, 1, 1, 1, 1, 0}, {1, 1, 1, 1, 1, 1, 1, 0}, {4, 3, 6, 5, 4, 3, 2, 2}, {0, 0, 0, 0, 0, 0, -1, 0}, {-3, -2, -4, -3, -2, -1, -1, -2}, {0, 0, 1, 1, 1, 1, 0, 0}, {1, 1, 1, 1, 1, 1, 0, 0}, {4, 3, 6, 5, 4, 3, 1, 2}, {1, 1, 2, 2, 2, 2, 1, 0}, {0, 0, 0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 0, -1, -1, 0}, {-3, -2, -4, -3, -2, -2, -1, -2}, {0, 0, 1, 1, 1, 0, 0, 0}, {1, 1, 1, 1, 1, 0, 0, 0}, {4, 3, 6, 5, 4, 2, 1, 2}, {1, 1, 2, 2, 2, 1, 1, 0}, {1, 1, 2, 2, 2, 1, 0, 0}, {0, 0, 0, 0, -1, 0, 0, 0}, {0, 0, 0, 0, -1, -1, 0, 0}, {0, 0, 0, 0, -1, -1, -1, 0}, {-3, -2, -4, -3, -3, -2, -1, -2}, {0, 0, 1, 1, 0, 0, 0, 0}, {1, 1, 1, 1, 0, 0, 0, 0}, {4, 3, 6, 5, 3, 2, 1, 2}, {1, 1, 2, 2, 1, 1, 1, 0}, {1, 1, 2, 2, 1, 1, 0, 0}, {1, 1, 2, 2, 1, 0, 0, 0}, {-1, 0, -1, -1, 0, 0, 0, 0}, {-1, 0, -1, -1, -1, 0, 0, 0}, {-1, 0, -1, -1, -1, -1, 0, 0}, {-1, 0, -1, -1, -1, -1, -1, 0}, {-4, -2, -5, -4, -3, -2, -1, -2}, {-1, 0, 0, 0, 0, 0, 0, 0}, { 0, 1, 0, 0, 0, 0, 0, 0}, {3, 3, 5, 4, 3, 2, 1, 2}, {0, 1, 1, 1, 1, 1, 1, 0}, {0, 1, 1, 1, 1, 1, 0, 0}, {0, 1, 1, 1, 1, 0, 0, 0}, {0, 1, 1, 1, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, -1, 0, 0, 0, 0}, {0, 0, 0, -1, -1, 0, 0, 0}, {0, 0, 0, -1, -1, -1, 0, 0}, { 0, 0, 0, -1, -1, -1, -1, 0}, {-3, -2, -4, -4, -3, -2, -1, -2}, {0, 0, 1, 0, 0, 0, 0, 0}, {1, 1, 1, 0, 0, 0, 0, 0}, {4, 3, 6, 4, 3, 2, 1, 2}, {1, 1, 2, 1, 1, 1, 1, 0}, {1, 1, 2, 1, 1, 1, 0, 0}, {1, 1, 2, 1, 1, 0, 0, 0}, {1, 1, 2, 1, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 0, 0}, {-1, 0, 0, 0, 0, 0, 0, -1}, {2, 2, 4, 3, 2, 1, 0, 1}, {-1, 0, -1, -1, -1, -1, -1, -1}, {2, 2, 4, 3, 2, 1, 1, 1}, {-1, 0, -1, -1, -1, -1, 0, -1}, {2, 2, 3, 2, 1, 0, 0, 1}, {2, 2, 4, 3, 2, 2, 1, 1}, {-1, 0, -1, -1, -1, 0, 0, -1}, {2, 2, 3, 2, 1, 1, 0, 1}, {2, 2, 3, 2, 1, 1, 1, 1}, {2, 2, 4, 3, 3, 2, 1, 1}, {-1, 0, -1, -1, 0, 0, 0, -1}, {2, 2, 3, 2, 2, 1, 0, 1}, {2, 2, 3, 2, 2, 1, 1, 1}, {2, 2, 3, 2, 2, 2, 1, 1}, {3, 2, 5, 4, 3, 2, 1, 1}, {0, 0, 0, 0, 0, 0, 0, -1}, {3, 2, 4, 3, 2, 1, 0, 1}, {3, 2, 4, 3, 2, 1, 1, 1}, {3, 2, 4, 3, 2, 2, 1, 1}, {3, 2, 4, 3, 3, 2, 1, 1}, {2, 2, 4, 4, 3, 2, 1, 1}, {-1, 0, -1, 0, 0, 0, 0, -1}, {2, 2, 3, 3, 2, 1, 0, 1}, {2, 2, 3, 3, 2, 1, 1, 1}, {2, 2, 3, 3, 2, 2, 1, 1}, {2, 2, 3, 3, 3, 2, 1, 1}, {3, 2, 4, 4, 3, 2, 1, 1}, { 1/2, 1/2, 1, 0, 0, 0, 0, 0}, {(-1)/2, 1/2, 0, 0, 0, 0, 0, 0}, { 1/2, 1/2, 1, 1, 0, 0, 0, 0}, {1/2, 1/2, 1, 1, 1, 0, 0, 0}, { 1/2, 1/2, 1, 1, 1, 1, 0, 0}, {1/2, 1/2, 1, 1, 1, 1, 1, 0}, { 7/2, 5/2, 5, 4, 3, 2, 1, 2}, {1/2, 1/2, 0, 0, 0, 0, 0, 0}, {3, 3, 5, 4, 3, 2, 1, 1}}, $CellContext`bitOrd = {5, 2, 1}, $CellContext`bitPerm = {{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}, $CellContext`bP = 1, $CellContext`dynkList = {{{{{{1, 2}, 1}}, {}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}}, {{{1, 2}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}}, {{{1, 2}, 1}, {{ 2, 3}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}}, {{{ 1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}}, {{{1, 2}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}}, {{{1, 2}, 1}, {{ 2, 3}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}}, {{{ 1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}, {{8, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{7, 8}, 2}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}}, {{{1, 2}, 2}, {{ 2, 3}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}}, {{{ 1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}}, {{{1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}}, {{{1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}}, {{{1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}, {{8, 2}, 0}}, {{{1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{7, 8}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{2, 3}, 0}}, {{{ 1, 2}, 1}, {{2, 3}, 1}, {{2, 4}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{3, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{3, 5}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{4, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{4, 6}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{5, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{5, 7}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}, {{6, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{6, 8}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{3, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{3, 6}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{4, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{4, 7}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}, {{5, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{5, 8}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}}, {{{ 1, 2}, 1}, {{2, 3}, 2}, {{3, 4}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}}, {{{1, 2}, 3}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}}, {{{1, 2}, 1}, {{ 2, 3}, 3}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}}, {{{ 1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 3}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}}, {{{1, 2}, 5}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}}, {{{1, 2}, 5}, {{ 2, 3}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}}, {{{ 1, 2}, 5}, {{2, 3}, 1}, {{3, 4}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}}, {{{1, 2}, 5}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}}, {{{1, 2}, 5}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{5, 2}, 0}, {{6, 2}, 0}, {{7, 2}, 0}}, {{{1, 2}, 5}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}}, 0}}, {{{{{1, 1}, 1}, {{2, 1}, 0}, {{3, 1}, 0}, {{4, 1}, 1}, {{5, 1}, 0}, {{6, 1}, 0}, {{7, 1}, 1}, {{8, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{7, 8}, 1}}, 0}, {{{{10, 1}, 1}, {{11, 1}, 0}, {{12, 1}, 1}, {{13, 1}, 0}, {{ 14, 1}, 1}, {{15, 1}, 0}, {{16, 1}, 1}, {{17, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{ 6, 7}, 1}, {{7, 8}, 2}}, 0}, {{{{1, 2}, 1}, {{2, 2}, 1}, {{3, 2}, 1}, {{4, 2}, 1}, {{5, 2}, 1}, {{6, 2}, 1}, {{7, 2}, 1}, {{8, 2}, 0}}, {{{1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{7, 8}, 1}}, 0}, {{{{10, 2}, 0}, {{11, 2}, 1}, {{12, 2}, 1}, {{13, 2}, 0}, {{ 14, 2}, 0}, {{15, 2}, 0}, {{16, 2}, 0}, {{15, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{ 6, 7}, 1}, {{6, 8}, 1}}, 0}, {{{{1, 3}, 1}, {{2, 3}, 1}, {{3, 3}, 0}, {{4, 3}, 0}, {{5, 3}, 0}, {{6, 3}, 0}, {{7, 3}, 0}, {{5, 4}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{5, 8}, 1}}, 0}, {{{{10, 3}, 0}, {{11, 3}, 0}, {{12, 3}, 1}, {{13, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 2}, {{3, 4}, 1}}, 0}, {{{{17, 3}, 0}, {{18, 3}, 1}}, {{{1, 2}, 3}}, 0}, {{{{10, 4}, 0}, {{11, 4}, 0}, {{12, 4}, 0}}, {{{1, 2}, 1}, {{ 2, 3}, 3}}, 0}, {{{{15, 4}, 1}, {{16, 4}, 1}, {{17, 4}, 1}, {{18, 4}, 1}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 3}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{2, 1}, 0}, {{1, 1}, 0}, {{3, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{4, 6}, 1}}, 0}, {{{{1, 3}, 1}, {{2, 3}, 0}, {{3, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 3}}, 0}, {{{{5, 2}, 1}, {{6, 2}, 0}, {{7, 2}, 0}, {{8, 3}, 0}, {{8, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{3, 5}, 1}}, 0}, {{{{5, 4}, 1}, {{6, 4}, 0}, {{7, 4}, 0}, {{8, 4}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 2}}, 0}, {{{{14, 1}, 1}, {{13, 1}, 0}, {{12, 2}, 0}, {{13, 3}, 0}, {{ 14, 3}, 0}, {{11, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{3, 6}, 1}}, 0}, {{{{11, 4}, 1}, {{12, 4}, 0}, {{13, 4}, 0}, {{14, 4}, 0}}, {{{1, 2}, 1}, {{2, 3}, 2}, {{3, 4}, 1}}, 0}, {{{{17, 1}, 1}, {{16, 2}, 0}, {{17, 3}, 0}, {{17, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{2, 4}, 1}}, 0}, {{{{16, 4}, 1}, {{17, 4}, 0}}, {{{1, 2}, 3}}, 0}}, {{{{{1, 2}, 1}, {{2, 2}, 0}, {{3, 2}, 0}, {{4, 2}, 0}, {{3, 1}, 0}, {{2, 1}, 0}, {{1, 1}, 0}, {{4, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}, {{5, 8}, 1}}, 0}, {{{{1, 3}, 1}, {{2, 3}, 0}, {{3, 3}, 0}, {{4, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 3}}, 0}, {{{{6, 1}, 1}, {{7, 2}, 0}, {{8, 1}, 0}, {{9, 2}, 0}, {{10, 1}, 0}, {{11, 2}, 0}, {{12, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}}, 0}, {{{{13, 2}, 1}, {{13, 1}, 0}}, {{{1, 2}, 4}}, 0}, {{{{8, 3}, 1}, {{9, 4}, 0}, {{10, 3}, 0}, {{11, 4}, 0}, {{12, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}}, 0}, {{{{13, 4}, 1}, {{13, 3}, 0}}, {{{1, 2}, 3}}, 0}, {{{{15, 1}, 1}, {{15, 2}, 0}, {{15, 3}, 0}, {{16, 4}, 0}, {{ 17, 3}, 0}, {{17, 2}, 0}, {{17, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 7}, 1}}, 0}, {{{{18, 4}, 1}, {{18, 3}, 0}, {{18, 2}, 0}, {{18, 1}, 0}}, {{{1, 2}, 2}, {{2, 3}, 1}, {{3, 4}, 1}}, 0}}, {{{{{1, 1}, 1}, {{1, 3}, 0}, {{2, 2}, 0}, {{3, 2}, 0}}, {{{ 1, 3}, 1}, {{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}}, 2}, {{{{4, 1}, 0}, {{5, 2}, 1}, {{6, 1}, 0}, {{4, 3}, 0}, {{6, 3}, 0}, {{7, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{2, 4}, 1}, {{2, 5}, 1}, {{5, 6}, 1}}, 2}, {{{{9, 2}, 1}, {{8, 2}, 1}, {{8, 4}, 0}, {{9, 4}, 0}, {{10, 3}, 0}, {{11, 3}, 0}, {{12, 3}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 1}, 1}, {{5, 6}, 1}, {{6, 7}, 1}}, 3}, {{{{12, 1}, 0}, {{13, 1}, 1}, {{14, 1}, 1}, {{15, 1}, 1}, {{ 16, 1}, 0}, {{14, 2}, 0}, {{17, 1}, 0}, {{18, 1}, 0}, {{19, 1}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{3, 6}, 1}, {{5, 7}, 1}, {{7, 8}, 1}, {{8, 9}, 1}}, 3}}, {{{{{1, 1}, 1}, {{1, 3}, 0}, {{2, 2}, 1}}, {{{1, 3}, 1}, {{ 1, 2}, 1}, {{2, 3}, 1}}, 1}, {{{{5, 1}, 0}, {{4, 2}, 0}, {{5, 3}, 0}, {{6, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 1}, 1}}, 1}, {{{{9, 1}, 0}, {{8, 1}, 1}, {{8, 3}, 0}, {{9, 3}, 0}, {{10, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 1}, 1}}, 1}, {{{{14, 1}, 1}, {{13, 1}, 0}, {{12, 2}, 0}, {{13, 3}, 0}, {{ 14, 3}, 0}, {{15, 2}, 0}}, {{{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{5, 6}, 1}, {{6, 1}, 1}}, 1}}, {{{{{5, 2}, 0}, {{4, 2}, 0}, {{3, 2}, 0}, {{2, 2}, 0}, {{1, 2}, 0}, {{6, 2}, 0}, {{6, 3}, 0}, {{6, 4}, 0}, {{6, 5}, 0}, {{ 5, 5}, 0}, {{7, 2}, 0}, {{8, 2}, 0}, {{9, 2}, 0}, {{10, 2}, 0}, {{11, 2}, 0}, {{5, 1}, 0}, {{6, 1}, 0}, {{7, 1}, 0}}, {{{ 16, 1}, 1}, {{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{17, 6}, 1}, {{6, 7}, 1}, {{7, 8}, 1}, {{8, 9}, 1}, {{9, 10}, 1}, {{18, 11}, 1}, {{11, 12}, 1}, {{12, 13}, 1}, {{13, 14}, 1}, {{14, 15}, 1}, {{16, 17}, 1}, {{17, 18}, 1}}, 3}}, {{{{{5, 2}, 0}, {{4, 2}, 0}, {{3, 2}, 0}, {{2, 2}, 0}, {{1, 2}, 0}, {{6, 2}, 0}, {{6, 3}, 0}, {{6, 4}, 0}, {{6, 5}, 0}, {{ 5, 5}, 0}, {{7, 2}, 0}, {{8, 2}, 0}, {{9, 2}, 0}, {{10, 2}, 0}, {{11, 2}, 0}, {{4, 1}, 0}, {{3, 1}, 0}, {{7, 3}, 0}, {{8, 3}, 0}, {{8, 1}, 0}, {{9, 1}, 0}, {{5, 1}, 0}, {{6, 1}, 0}, {{ 7, 1}, 0}}, {{{22, 1}, 1}, {{1, 2}, 1}, {{2, 3}, 1}, {{3, 4}, 1}, {{4, 5}, 1}, {{23, 6}, 1}, {{6, 7}, 1}, {{7, 8}, 1}, {{8, 9}, 1}, {{9, 10}, 1}, {{24, 11}, 1}, {{11, 12}, 1}, {{12, 13}, 1}, {{13, 14}, 1}, {{14, 15}, 1}, {{1, 16}, 1}, {{16, 17}, 1}, {{6, 18}, 1}, {{18, 19}, 1}, {{11, 20}, 1}, {{20, 21}, 1}, {{22, 23}, 1}, {{23, 24}, 1}}, 3}}}, $CellContext`subGroups = { "a1", "a2", "a3", "a4", "a5", "a6", "a7", "b2", "b3", "b4", "b5", "b6", "b7", "b8", "c3", "c4", "c5", "c6", "c7", "c8", "d4", "d5", "d6", "d7", "d8", "e6", "e7", "e8", "f4", "g2", "h3", "h4", "cube2", "cube3", "cube4", "cube5", "cube6", "cube7", "finite1", "folded1", "folded2", "extended1", "looped1", "monster1", "monster2"}, $CellContext`doE8 := With[{$CellContext`local$ = $CellContext`localE8}, Module[$CellContext`local$, $CellContext`p3DList = { " 2D", " 3D", " Stereo", " Anaglyph"}; $CellContext`needsArtPrint := And[$CellContext`artPrint$$, $CellContext`fileOut$$]; \ $CellContext`needsAnim8 := And[ Not[$CellContext`useDimLocs$$], Or[$CellContext`steps$$ > 1, And[$CellContext`showEdges$$, Or[$CellContext`eSteps$$ > 1, $CellContext`anim8EdgeList$$]]]]; \ $CellContext`needsEdges := Or[$CellContext`showEdges$$, $CellContext`showClickVerts$$, \ $CellContext`ltps$$ != {}]; $CellContext`clearClickVerts := \ ($CellContext`plines$$ = {}; $CellContext`vlines$$ = {}; \ $CellContext`vLineColors$$ = {}; $CellContext`ltps$$ = {}; \ $CellContext`showClickVerts$$ = False); $CellContext`plDims := If[$CellContext`p3D$$ == First[$CellContext`p3DList], 2, 3]; $CellContext`dimZeros := Array[0& , {$CellContext`plDims}]; $CellContext`zeroPt := Point[$CellContext`dimZeros]; $CellContext`nullPt := { PointSize[0], Opacity[0], White, Point[$CellContext`dimZeros]}; $CellContext`axesPt := { PointSize[0.01], Black, Point[$CellContext`dimZeros]}; $CellContext`faceList := \ {{$CellContext`H$$, $CellContext`V$$, $CellContext`Z$$}, {$CellContext`Z$$, \ $CellContext`H$$, $CellContext`V$$}, {$CellContext`V$$, $CellContext`Z$$, \ $CellContext`H$$}}; $CellContext`ptCds := Part[$CellContext`faceList, $CellContext`face$$, {1, 2, 3}]; $CellContext`setPTcd[ Pattern[$CellContext`in$, Blank[]]] := ($CellContext`H$$ = Part[$CellContext`in$, 1]; $CellContext`V$$ = Part[$CellContext`in$, 2]; $CellContext`Z$$ = Part[$CellContext`in$, 3]); $CellContext`initLocPtCds := ($CellContext`locPtCdArr$$ = Transpose[ Part[ Subscript[$CellContext`ptCds, $CellContext`scaled], Span[ 1, 2]]]; $CellContext`locPtCdTrk$$ = \ $CellContext`locPtCdArr$$); $CellContext`outerDims[ Pattern[$CellContext`inDims$, Blank[]]] := If[($CellContext`outerSum = Chop[$CellContext`nDcamera$$ ($CellContext`dimTrim$$ - \ $CellContext`plDims) + Total[ Map[ Part[$CellContext`newLoc, #]& , $CellContext`outerDim = If[ And[$CellContext`dimTrim$$ - $CellContext`plDims > 1, Length[$CellContext`inDims$] >= $CellContext`plDims], If[Union[ Range[$CellContext`dimTrim$$], Part[$CellContext`inDims$, Span[1, $CellContext`plDims]]] == Range[$CellContext`dimTrim$$], Complement[ Range[$CellContext`dimTrim$$], $CellContext`inDims$], \ {$CellContext`dimTrim$$}], {$CellContext`dimTrim$$}]]]]) == 0, $CellContext`outerSum = $CellContext`chop, \ $CellContext`outerSum]; $CellContext`transOuter[ Pattern[$CellContext`inDims$, Blank[]]] := ($CellContext`outerDims[$CellContext`inDims$]; Map[(Part[$CellContext`newLoc, #] = Part[$CellContext`newLoc, #] + $CellContext`nDcamera$$ + \ #/$CellContext`dims)& , $CellContext`outerDim]); $CellContext`posDiff[ Pattern[$CellContext`inDims$, Blank[]]] := ($CellContext`outerDims[$CellContext`inDims$]; 2 $CellContext`nDcamera$$ (($CellContext`dimTrim$$ - \ $CellContext`plDims)/$CellContext`outerSum)); $CellContext`posTbl[ Pattern[$CellContext`loc$, Blank[]]] := Map[($CellContext`newLoc = $CellContext`loc$; If[$CellContext`steps$$ > 1, Switch[$CellContext`pthRot$$, "Rot", $CellContext`newLoc = Dot[$CellContext`loc$, $CellContext`rotXYZ[ $CellContext`nDRot[$CellContext`\[Theta]]]]]]; If[$CellContext`perspective$$, $CellContext`transOuter[ Union[$CellContext`dlXn, $CellContext`dlYn, \ $CellContext`dlZn]]; Part[$CellContext`newLoc, First[$CellContext`dlXn]] = Part[$CellContext`newLoc, First[$CellContext`dlXn]] \ $CellContext`posDiff[$CellContext`dlXn]; Part[$CellContext`newLoc, First[$CellContext`dlYn]] = Part[$CellContext`newLoc, First[$CellContext`dlYn]] \ $CellContext`posDiff[$CellContext`dlYn]; Part[$CellContext`newLoc, First[$CellContext`dlZn]] = Part[$CellContext`newLoc, First[$CellContext`dlZn]] \ $CellContext`posDiff[$CellContext`dlZn]]; If[ And[$CellContext`limitToRange$$, Dot[$CellContext`newLoc, Part[$CellContext`ptCds, #]] < Part[$CellContext`pt$$, #] - Subscript[$CellContext`range$$, $CellContext`scaled]], Part[$CellContext`pt$$, #] - Subscript[$CellContext`range$$, $CellContext`scaled], If[ And[$CellContext`limitToRange$$, Dot[$CellContext`newLoc, Part[$CellContext`ptCds, #]] > Part[$CellContext`pt$$, #] + Subscript[$CellContext`range$$, $CellContext`scaled]], Part[$CellContext`pt$$, #] + Subscript[$CellContext`range$$, $CellContext`scaled], Round[ Dot[$CellContext`newLoc, Part[$CellContext`ptCds, #]], $CellContext`chop]]])& , Range[$CellContext`plDims]]; $CellContext`dsGet[ Pattern[$CellContext`p$, Blank[]]] := If[$CellContext`ds$$ < 5, Switch[$CellContext`ds$$, 1, $CellContext`pBin[$CellContext`p$], 2, $CellContext`pE8[$CellContext`p$], 3, $CellContext`pPhys[$CellContext`p$], 4, $CellContext`pC600[$CellContext`p$]], Part[$CellContext`e8b, $CellContext`p$, $CellContext`ds$$ - 4]]; $CellContext`pPos[ Pattern[$CellContext`p, Blank[]]] := $CellContext`posTbl[ $CellContext`dsGet[$CellContext`p]]; $CellContext`e8ListInit := \ ($CellContext`scale$$ = 0.02; $CellContext`cylR$$ = 0.01; $CellContext`tickNum$$ = 4; $CellContext`range$$ = 1.5; $CellContext`pt$$ = {0, 0, 0}; $CellContext`zoom$$ = 0; $CellContext`favorite$$ = 15; $CellContext`pGrad$$ = 0; $CellContext`face$$ = 1; $CellContext`nDcamera$$ = 1.; $CellContext`steps$$ = 1; $CellContext`artPrint$$ = False; $CellContext`limitToRange$$ = True; $CellContext`perspective$$ = False; $CellContext`showAxes$$ = True; $CellContext`showPartVert$$ = True; $CellContext`showEdges$$ = False; $CellContext`showPolySurfaces$$ = False; $CellContext`showSurfaces$$ = False; $CellContext`showPvecs$$ = False; $CellContext`showPtext$$ = False; $CellContext`showPlocs$$ = False; $CellContext`showPmass$$ = False; $CellContext`showPerim$$ = False; $CellContext`showClr$$ = False; $CellContext`showClickVerts$$ = False; $CellContext`vOverlapColor$$ = False; $CellContext`physics$$ = False; $CellContext`ltps$$ = {}; $CellContext`useDimLocs$$ = False; $CellContext`perm = "Parent"; $CellContext`lie$$ = ""; $CellContext`ds$$ = 2; $CellContext`eGrad$$ = 10; $CellContext`edgeVals$$ = {{ Sqrt[2], 6720}}; $CellContext`anim8EdgeList$$ = False; $CellContext`eSteps$$ = 1; $CellContext`eColorPos$$ = True; $CellContext`eWnd$$ = $CellContext`eLim$$; \ $CellContext`rectification$$ = 0; $CellContext`dimTrim$$ = $CellContext`dims; \ $CellContext`innerMag$$ = 0; $CellContext`tT$$ = {}; $CellContext`XY$$ = {1, 1, 1} 20); $CellContext`e8ExtrasInit := \ ($CellContext`selCoxeterTrk$$ = ($CellContext`selCoxeter$$ = ""); $CellContext`pSize$$ = $CellContext`nrml; \ $CellContext`pListName$$ = "E8=!Excluded"; $CellContext`dsName$$ = "e8"; $CellContext`p3D$$ = " 2D"; $CellContext`auxFile$$ = "./auxData.xls"; $CellContext`fileOnly$$ = False; $CellContext`fileOut$$ = False; $CellContext`outFileDir$$ = "./"; $CellContext`outFile$$ = "E8out"; $CellContext`outFileType$$ = ".png"); $CellContext`setPthPrm := ($CellContext`pthRot$$ = "Trans&Rot"; $CellContext`pthPtCds$$ = "Identity"; $CellContext`dlXs$$ = $CellContext`dls[{ 5}]; $CellContext`dlYs$$ = $CellContext`dls[{ 6}]; $CellContext`dlZs$$ = $CellContext`dls[{ 7}]); $CellContext`clearPath := ( If[$CellContext`newPTcd$$ != {}, \ $CellContext`setPTcd[$CellContext`newPTcd$$]; $CellContext`newPTcd$$ = {}, If[$CellContext`favoriteTrk$$ != $CellContext`favorite$$, \ $CellContext`setPTcd[ Part[$CellContext`favorites, $CellContext`favorite$$]]; \ $CellContext`favoriteTrk$$ = $CellContext`favorite$$]]; \ $CellContext`setPthPrm; $CellContext`xy$$ = {1, 1}; $CellContext`zz$$ = 1; $CellContext`xyVwPnt$$ = {1.3, 2.4}; $CellContext`zVwPnt$$ = 2; $CellContext`nDRot[ Pattern[$CellContext`\[Theta], Blank[]]] := Part[ $CellContext`nDRots[$CellContext`\[Theta]], 1]; $CellContext`initLocPtCds); $CellContext`dobAND1[ Pattern[$CellContext`in, Blank[]]] := Switch[$CellContext`in, "E8 hexes", $CellContext`E8Hexes, "E8 hyper", $CellContext`E8Hyper, "E8 3", $CellContext`E83, "E8 3D", $CellContext`E83D, "E8 24x10", $CellContext`E824x10, "E8 12x5", $CellContext`E812x5, "E8 Petrie", $CellContext`E8Petrie, "E8 in E6", $CellContext`E8inE6, "E7", $CellContext`E7, "E6", $CellContext`E6, "E6 a", $CellContext`E6a, "E5", $CellContext`E5, "E4", $CellContext`E4, "F4", $CellContext`F4, "H4", $CellContext`H4a, "G2", $CellContext`G2, "Tesseract", $CellContext`Tesseract, "16 cell", $CellContext`Cell16, "24 cell", $CellContext`Cell24, "24 cell D4", $CellContext`Cell24D4, "24 cell G2", $CellContext`Cell24G2, "600 cell 3D", $CellContext`C6003D, "Hydrogen", $CellContext`Hydrogen, "none", $CellContext`none, "120 cell 2D squ", $CellContext`c1202DSquare, "120 cell 2D pent", $CellContext`c1202DPent, "120 cell 3D", $CellContext`c1203D, "600 cell 2D Petrie", $CellContext`c6002DPetrie, "600 cell 2D pent", $CellContext`c6002DPent, "600 cell 2D hex", $CellContext`c6002DHex, "600 cell 3D", $CellContext`c6003D, "input file", $CellContext`inFile]; $CellContext`dobAND2[ Pattern[$CellContext`in, Blank[]]] := Switch[$CellContext`in, "F4 tris", $CellContext`F4Tris, "F4 to G2", $CellContext`F4G2, "F4 star", $CellContext`F4Star, "2 cube Pascal", $CellContext`Cube2Pascal, "3 cube Pascal", $CellContext`Cube3Pascal, "4 cube Pascal", $CellContext`Cube4Pascal, "5 cube Pascal", $CellContext`Cube5Pascal, "6 cube Pascal", $CellContext`Cube6Pascal, "7 cube Pascal", $CellContext`Cube7Pascal, "8 cube Pascal", $CellContext`Cube8Pascal, "2 cube Petrie", $CellContext`Cube2Petrie, "3 cube Petrie", $CellContext`Cube3Petrie, "4 cube Petrie", $CellContext`Cube4Petrie, "5 cube Petrie", $CellContext`Cube5Petrie, "6 cube Petrie", $CellContext`Cube6Petrie, "7 cube Petrie", $CellContext`Cube7Petrie, "8 cube Petrie", $CellContext`Cube8Petrie, "lepton info", $CellContext`LeptonInfo, "quark info", $CellContext`QuarkInfo, "quark column", $CellContext`QuarkCol, "binary", $CellContext`Binary, "binary star", $CellContext`BinStar, "binary square", $CellContext`BinSquare, "devolution", $CellContext`Devolution, "XLS data file", $CellContext`auxXLS]; $CellContext`E8 := { If[$CellContext`auxData$$ == True, $CellContext`initAnim8]; $CellContext`e8ListInit; \ $CellContext`e8ExtrasInit; $CellContext`dispArr$$ = Array["?"& , $CellContext`le8]; Part[$CellContext`pls, 1] = Range[$CellContext`le8]; $CellContext`fltrdSubPlot$$ = Part[$CellContext`pls, 2]; $CellContext`clearFilter; $CellContext`clearPath; \ $CellContext`clearClickVerts}; $CellContext`E8Hexes := \ {$CellContext`favorite$$ = 21; $CellContext`scale$$ = 0.04; $CellContext`range$$ = 2.1; $CellContext`cylR$$ = 0.001; $CellContext`tT$$ = Part[$CellContext`triList, {4, 6}]; $CellContext`physics$$ = True; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`dlXs$$ = $CellContext`dls[{ 5}]; $CellContext`dlYs$$ = $CellContext`dls[{ 6}]; $CellContext`dlZs$$ = $CellContext`dls[{ 7}]}; $CellContext`E8Hyper := {$CellContext`favorite$$ = 23; $CellContext`tT$$ = Part[$CellContext`triList, {4, 6}]; $CellContext`physics$$ = True; $CellContext`face$$ = 1; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`dlXs$$ = $CellContext`dls[{ 5}]; $CellContext`dlYs$$ = $CellContext`dls[{ 6}]; $CellContext`dlZs$$ = $CellContext`dls[{ 7}]}; $CellContext`E83 := {$CellContext`favorite$$ = 26; $CellContext`tT$$ = Part[$CellContext`triList, {2, 4, 6}]; $CellContext`physics$$ = True; $CellContext`pthRot$$ = "Rot"; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`E83D := {$CellContext`scale$$ = 0.04; $CellContext`cylR$$ = 0.001; $CellContext`range$$ = 1.21; $CellContext`limitToRange$$ = False; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 0; $CellContext`p3D$$ = " 3D"}; $CellContext`E824x10 := {$CellContext`favorite$$ = 24}; $CellContext`E812x5 := {$CellContext`favorite$$ = 18; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 16; $CellContext`ds$$ = 3; $CellContext`dsName$$ = "physics"; $CellContext`dlXs$$ = $CellContext`dls[{ 5}]; $CellContext`dlYs$$ = $CellContext`dls[{ 6}]; $CellContext`dlZs$$ = $CellContext`dls[{ 7}]}; $CellContext`E8Petrie := {$CellContext`cylR$$ = 0.001; $CellContext`eGrad$$ = 51; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True}; $CellContext`E8inE6 := {$CellContext`scale$$ = 0.04; $CellContext`favorite$$ = 22; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 16}; $CellContext`E7 := {$CellContext`scale$$ = 0.04; $CellContext`favorite$$ = 2; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 16; $CellContext`edgeVals$$ = {{ Sqrt[2], 2164}}; $CellContext`pListName$$ = "E7"}; $CellContext`E6 := {$CellContext`scale$$ = 0.04; $CellContext`favorite$$ = 22; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 16; $CellContext`edgeVals$$ = {{ Sqrt[2], 800}}; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "E6"}; $CellContext`E6a := {$CellContext`pListName$$ = "E6"; $CellContext`doProj[6]; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 0}; $CellContext`E5 := {$CellContext`pListName$$ = "E5"; $CellContext`favorite$$ = 22; $CellContext`eSteps$$ = 5; $CellContext`eWnd$$ = 50; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 0}; $CellContext`E4 := {$CellContext`pListName$$ = "A4=SL(5)=E4"; $CellContext`favorite$$ = 27; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 0}; $CellContext`F4 := {$CellContext`favorite$$ = 21; $CellContext`range$$ = 2.1; $CellContext`showAxes$$ = False; $CellContext`edgeVals$$ = {{ Sqrt[2], 364}}; $CellContext`tT$$ = { "T4p"}; $CellContext`physics$$ = True; $CellContext`ds$$ = 3; $CellContext`pListName$$ = "F4"; $CellContext`dsName$$ = "physics"; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`H4a := {$CellContext`pListName$$ = "H4"; $CellContext`edgeVals$$ = {{ Sqrt[2], 1980}}; $CellContext`showEdges$$ = True}; $CellContext`G2 := {$CellContext`outFile$$ = "G2_"; $CellContext`outFileType$$ = First[$CellContext`fileTypeList]; $CellContext`scale$$ = 1/10.; $CellContext`physics$$ = True; $CellContext`showEdges$$ = True; $CellContext`showPvecs$$ = True; $CellContext`showPtext$$ = True; $CellContext`pListName$$ = "G2s=gluons"; $CellContext`dlXs$$ = $CellContext`dls[{ 3}]; $CellContext`dlYs$$ = $CellContext`dls[{ 6}]; $CellContext`dlZs$$ = $CellContext`dls[{ 7}]; $CellContext`pthRot$$ = "Trans&Rot"; $CellContext`steps$$ = 5; $CellContext`pthPtCds$$ = "PtCoords"}; $CellContext`Tesseract := \ {$CellContext`artPrint$$ = True; $CellContext`scale$$ = 0.1; $CellContext`limitToRange$$ = False; $CellContext`cylR$$ = 0.022; $CellContext`favorite$$ = 1; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 0; $CellContext`eColorPos$$ = False; $CellContext`edgeVals$$ = {{1, 32}}; $CellContext`dimTrim$$ = 4; $CellContext`vOverlapColor$$ = True; $CellContext`range$$ = 2; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]; $CellContext`xyVwPnt$$ = {0.6, 1.7}; $CellContext`zVwPnt$$ = 1/2; $CellContext`pthRot$$ = "Rot"; $CellContext`steps$$ = 5; $CellContext`pListName$$ = "8Cell=4Cube"; $CellContext`perspective$$ = True; $CellContext`nDcamera$$ = 2.; $CellContext`p3D$$ = " 3D"}; $CellContext`Cell16 := {$CellContext`pListName$$ = "16Cell"; $CellContext`p3D$$ = " 3D"; $CellContext`vOverlapColor$$ = True; $CellContext`dimTrim$$ = 4; $CellContext`limitToRange$$ = False; $CellContext`favorite$$ = 1; $CellContext`xyVwPnt$$ = {1, 1} (3/ 4.); $CellContext`zVwPnt$$ = 3/4.; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 0; $CellContext`edgeVals$$ = {{ Sqrt[2], 64}}}; $CellContext`Cell24 := {$CellContext`pListName$$ = "24Cell"; $CellContext`favorite$$ = 9; $CellContext`dimTrim$$ = 4; $CellContext`edgeVals$$ = {{1, 96}}; $CellContext`limitToRange$$ = False; $CellContext`nDcamera$$ = 1.; $CellContext`xyVwPnt$$ = {1, 1} (3/ 4.); $CellContext`zVwPnt$$ = 3/4.; $CellContext`pthRot$$ = "Rot"; $CellContext`nDRot[ Pattern[$CellContext`\[Theta], Blank[]]] := Part[ $CellContext`nDRots[$CellContext`\[Theta]], 2]; $CellContext`p3D$$ = " 3D"; $CellContext`showEdges$$ = True}; $CellContext`Cell24D4 := {$CellContext`scale$$ = 0.04; $CellContext`cylR$$ = 0.021; $CellContext`favorite$$ = 9; $CellContext`dimTrim$$ = 4; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`eGrad$$ = 16; $CellContext`edgeVals$$ = {{ Sqrt[2], 96}}; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "D4=SO(8)"}; $CellContext`Cell24G2 := \ {$CellContext`pListName$$ = "pType"; $CellContext`favorite$$ = 9; $CellContext`dimTrim$$ = 4; $CellContext`showEdges$$ = True; $CellContext`limitToRange$$ = False; $CellContext`nDcamera$$ = 1.; $CellContext`xyVwPnt$$ = {1, 1} (3/ 4.); $CellContext`zVwPnt$$ = 3/4.; $CellContext`range$$ = 1.5; $CellContext`pthRot$$ = "Rot"; $CellContext`p3D$$ = " 3D"; $CellContext`fr$$ = {3, 4}}; $CellContext`C6003D := {$CellContext`range$$ = 1.; $CellContext`showEdges$$ = True; $CellContext`edgeVals$$ = {{1, 928}}; $CellContext`ds$$ = 4; $CellContext`dsName$$ = "CELL600"; $CellContext`showPolySurfaces$$ = True; $CellContext`p3D$$ = " 3D"; $CellContext`H$$ = {1, 0, 0, 0, 0, 0, 0, 0}/ 2; $CellContext`V$$ = {0, 1, 0, 0, 0, 0, 0, 0}/ 2; $CellContext`Z$$ = {0, 0, 0, 1, 0, 0, 0, 0}/ 2; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 4}]}; $CellContext`Hydrogen := {$CellContext`scale$$ = 0.54; $CellContext`cylR$$ = 0.026; $CellContext`favorite$$ = 3; $CellContext`pthRot$$ = "Trans"; $CellContext`physics$$ = True; $CellContext`showAxes$$ = False; $CellContext`showEdges$$ = True; $CellContext`showPtext$$ = True; $CellContext`eGrad$$ = 44; $CellContext`edgeVals$$ = {{ "All", 6}}; $CellContext`pListName$$ = "None"; $CellContext`ds$$ = 3; $CellContext`dsName$$ = "physics"; $CellContext`showPolySurfaces$$ = True; $CellContext`xyVwPnt$$ = {1, 1} (3/ 4.); $CellContext`zVwPnt$$ = 3/4.; $CellContext`p3D$$ = " 3D"; $CellContext`addParticles[$CellContext`hydrogen]; \ $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]; $CellContext`steps$$ = 5}; $CellContext`none := {$CellContext`pListName$$ = Last[$CellContext`plNames]; $CellContext`favorite$$ = 23; $CellContext`edgeVals$$ = { If[ AtomQ[$CellContext`edgeList$$], {}, Last[$CellContext`edgeList$$]]}; $CellContext`p3D$$ = Part[$CellContext`p3DList, 2]; $CellContext`physics$$ = True; $CellContext`xyVwPnt$$ = {1., 1.}; $CellContext`zVwPnt$$ = 1.; $CellContext`scale$$ = 1/10.; $CellContext`showEdges$$ = True; $CellContext`showPtext$$ = True; $CellContext`tT$$ = Part[$CellContext`triList, {2, 4, 6}]; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`F4Tris := {$CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`favorite$$ = 19; $CellContext`physics$$ = True; $CellContext`tT$$ = { Part[$CellContext`triList, 2]}; $CellContext`pthRot$$ = "Trans&Rot"; $CellContext`dlXs$$ = $CellContext`dls[{ 4}]; $CellContext`dlYs$$ = $CellContext`dls[{ 3}]; $CellContext`dlZs$$ = $CellContext`dls[{ 1}]; $CellContext`steps$$ = 5}; $CellContext`F4G2 := {$CellContext`favorite$$ = 12; $CellContext`physics$$ = True; $CellContext`tT$$ = { Part[$CellContext`triList, 2], Part[$CellContext`triList, 6]}; $CellContext`pthRot$$ = "Trans"; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`dlXs$$ = $CellContext`dls[{ 4}]; $CellContext`dlYs$$ = $CellContext`dls[{ 3}]; $CellContext`dlZs$$ = $CellContext`dls[{ 1}]; $CellContext`steps$$ = 5}; $CellContext`F4Star := {$CellContext`artPrint$$ = True; $CellContext`limitToRange$$ = False; $CellContext`favorite$$ = 21; $CellContext`pGrad$$ = 16; $CellContext`showAxes$$ = False; $CellContext`tT$$ = {"T4p"}; $CellContext`ds$$ = 3; $CellContext`dsName$$ = "physics"; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`Cube2Pascal := {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 4}}; $CellContext`dimTrim$$ = 2; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "B2=SO(5)=C2"; $CellContext`doCubePascal[ 2]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`Cube3Pascal := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 12}}; $CellContext`dimTrim$$ = 3; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "3Cube"; $CellContext`doCubePascal[ 3]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`Cube4Pascal := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`favorite$$ = 27; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 32}}; $CellContext`dimTrim$$ = 4; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "8Cell=4Cube"}; $CellContext`Cube5Pascal := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`favorite$$ = 28; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 80}}; $CellContext`dimTrim$$ = 5; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "C4=5Cube"}; $CellContext`Cube6Pascal := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 192}}; $CellContext`dimTrim$$ = 6; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "6Cube=Hexeract"; $CellContext`doCubePascal[ 6]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`Cube7Pascal := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`range$$ = 2.; $CellContext`limitToRange$$ = False; $CellContext`favorite$$ = 29; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 448}}; $CellContext`dimTrim$$ = 7; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "C8=7Cube=Int/2"}; $CellContext`Cube8Pascal := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 128}}; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "All"; $CellContext`doCubePascal[ 8]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`Cube2Petrie := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.019; $CellContext`favorite$$ = 1; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 12}}; $CellContext`dimTrim$$ = 2; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "B2=SO(5)=C2"}; $CellContext`Cube3Petrie := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.019; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 12}}; $CellContext`dimTrim$$ = 3; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "3Cube"; $CellContext`doCube[ 3]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`Cube4Petrie := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`favorite$$ = 9; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 32}}; $CellContext`dimTrim$$ = 4; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "8Cell=4Cube"}; $CellContext`Cube5Petrie := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`favorite$$ = 10; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 80}}; $CellContext`dimTrim$$ = 5; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "C4=5Cube"}; $CellContext`Cube6Petrie := \ {$CellContext`scale$$ = 0.06; $CellContext`cylR$$ = 0.021; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 192}}; $CellContext`dimTrim$$ = 6; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "6Cube=Hexeract"; $CellContext`doCube[ 6]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`Cube7Petrie := \ {$CellContext`scale$$ = 0.04; $CellContext`favorite$$ = 11; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 448}}; $CellContext`dimTrim$$ = 7; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "C8=7Cube=Int/2"}; $CellContext`Cube8Petrie := \ {$CellContext`scale$$ = 0.04; $CellContext`showEdges$$ = True; $CellContext`pGrad$$ = 10; $CellContext`edgeVals$$ = {{1, 128}}; $CellContext`vOverlapColor$$ = True; $CellContext`pListName$$ = "All"; $CellContext`doCube[ 8]; $CellContext`newPTcd$$ = {$CellContext`H$$, \ $CellContext`V$$, $CellContext`Z$$}}; $CellContext`LeptonInfo := \ {$CellContext`scale$$ = 1/10.; $CellContext`showPtext$$ = True; $CellContext`physics$$ = True; $CellContext`showPmass$$ = True; $CellContext`pListName$$ = "none"; $CellContext`addParticles[$CellContext`l1]}; \ $CellContext`QuarkInfo := {$CellContext`scale$$ = 1/10.; $CellContext`favorite$$ = 20; $CellContext`p3D$$ = Part[$CellContext`p3DList, 2]; $CellContext`physics$$ = True; $CellContext`xyVwPnt$$ = {1, 1} (3/ 4.); $CellContext`zVwPnt$$ = 3/4.; $CellContext`showSurfaces$$ = True; $CellContext`showPtext$$ = True; $CellContext`showPmass$$ = True; $CellContext`fr$$ = 2; $CellContext`fa$$ = 0; $CellContext`fc$$ = 1; $CellContext`fs$$ = 0}; $CellContext`QuarkCol := {$CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 3]; $CellContext`scale$$ = 1/10.; $CellContext`favorite$$ = 31; $CellContext`physics$$ = True; $CellContext`p3D$$ = Part[$CellContext`p3DList, 2]; $CellContext`pthRot$$ = "Trans"; $CellContext`dlXs$$ = \ $CellContext`dls[$CellContext`H1a]; $CellContext`dlYs$$ = \ $CellContext`dls[$CellContext`V1a]; $CellContext`dlZs$$ = \ $CellContext`dls[$CellContext`Z1a]; $CellContext`tT$$ = $CellContext`triList; \ $CellContext`steps$$ = 5; $CellContext`pListName$$ = "none"; $CellContext`addParticles[$CellContext`q]}; \ $CellContext`Binary := {$CellContext`range$$ = 1.25; $CellContext`favorite$$ = 25; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 1]; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`BinStar := {$CellContext`pt$$ = {1, 1, 1} ($CellContext`range$$/2); $CellContext`favorite$$ = 9; $CellContext`showEdges$$ = True; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 1]; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`BinSquare := {$CellContext`range$$ = 1.25; $CellContext`favorite$$ = 23; $CellContext`dsName$$ = Part[$CellContext`dsNames, $CellContext`ds$$ = 1]; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]}; $CellContext`Devolution := {$CellContext`scale$$ = 0.04; $CellContext`cylR$$ = 0.008; $CellContext`range$$ = 2.; $CellContext`limitToRange$$ = False; $CellContext`favorite$$ = 23; $CellContext`physics$$ = True; $CellContext`ds$$ = 3; $CellContext`dsName$$ = "physics"; $CellContext`xyVwPnt$$ = {1, 1} (3/ 4.); $CellContext`zVwPnt$$ = 3/4.; $CellContext`dlXs$$ = $CellContext`dls[{ 1}]; $CellContext`dlYs$$ = $CellContext`dls[{ 2}]; $CellContext`dlZs$$ = $CellContext`dls[{ 3}]; $CellContext`p3D$$ = " 3D"; $CellContext`ltps$$ = {61, 195}; $CellContext`plines$$ = CompressedData[" 1:eJwNw8tPAQAAB2CrzZqtQ/OYQwc6mKONFuonR4tC/0ByIbEmbTjQqTxu6XWI VevW88ix9UOpZY42N3QJ49LM5pBv+5TuvU33lEAgOJicnsTMGLNDyAeY70PR g7KLhQ5UdWiq0L1iMY+lF+ifYXiC8RHLD1i5h8mJVQssq3CaELhD8Bb7Nwhd I5xDJIvoFWKXiF/g8Bznh7iI4zKGqyiyEeTCuA7hZh+3QdwFcL+Ch2U8GvFk wLMeL0vIL+JVh6oGdRU6C+gq0VOgP4+BHMNZjGcoHFH0x7lfin8oaVPaoqxJ dYPaGs3fXPui9ZO2Ctc/uPFOe5mOEp1Fbp3RdcrtDN0n9KTpTXEnSV+Cu8f0 H/HIz+NdJnxM7jDlZdrDEzcz2zx18WyLhTe+FVh0suRg2c73DX6ss2Ljp5Vf a/w2s6ZlQ82mjC0p2xL+iPk7xz8RR8J/7GyvzA== "]}; $CellContext`setLieGroup := ( Map[(Part[$CellContext`dispArr$$, #] = "n")& , Range[$CellContext`le8]]; Map[{Part[$CellContext`dispArr$$, #] = "y"}& , Switch[ ToLowerCase[$CellContext`lie$$], "a1", $CellContext`a1, "a2", $CellContext`a2, "a3", $CellContext`a3, "a4", $CellContext`a4, "a5", $CellContext`a5, "a6", $CellContext`a6, "a7", $CellContext`a7, "b2", $CellContext`b2, "b3", $CellContext`b3, "b4", $CellContext`b4, "b5", $CellContext`b5, "b6", $CellContext`b6, "b8", $CellContext`b8, "c3", $CellContext`c3, "c4", $CellContext`c4, "c5", $CellContext`c5, "c6", $CellContext`c6, "c7", $CellContext`c7, "c8", $CellContext`c8, "d4", $CellContext`d4, "d5", $CellContext`d5, "d6", $CellContext`d6, "d7", $CellContext`d7, "d8", $CellContext`d8, "e6", $CellContext`e6, "e7", $CellContext`e7, "e8", $CellContext`e8, "g2", $CellContext`g2, "f4", $CellContext`f4, "h4", $CellContext`h4]]); $CellContext`filterList := \ {$CellContext`fa$$, $CellContext`fp$$, $CellContext`fc$$, $CellContext`fs$$, \ $CellContext`fg$$, $CellContext`fr$$}; $CellContext`setFlt := \ ($CellContext`fa$$ = {}; $CellContext`fp$$ = {}; $CellContext`fc$$ = {}; \ $CellContext`fs$$ = {}; $CellContext`fg$$ = {}; $CellContext`fr$$ = {}); \ $CellContext`unsetFlt := (Unset[$CellContext`fa$$]; Unset[$CellContext`fp$$]; Unset[$CellContext`fc$$]; Unset[$CellContext`fs$$]; Unset[$CellContext`fg$$]; Unset[$CellContext`fr$$]); $CellContext`ifNum := \ ($CellContext`fa$$ = If[ NumberQ[$CellContext`fa$$], {$CellContext`fa$$}, {}]; \ $CellContext`fp$$ = If[ NumberQ[$CellContext`fp$$], {$CellContext`fp$$}, {}]; \ $CellContext`fc$$ = If[ NumberQ[$CellContext`fc$$], {$CellContext`fc$$}, {}]; \ $CellContext`fs$$ = If[ NumberQ[$CellContext`fs$$], {$CellContext`fs$$}, {}]; \ $CellContext`fg$$ = If[ NumberQ[$CellContext`fg$$], {$CellContext`fg$$}, {}]; \ $CellContext`fr$$ = If[ NumberQ[$CellContext`fr$$], {$CellContext`fr$$}, {}]); \ $CellContext`ifLen := (If[ And[ ListQ[$CellContext`fa$$], $CellContext`fa$$ != {}], \ $CellContext`fa$$ = First[$CellContext`fa$$], Unset[$CellContext`fa$$]]; If[ And[ ListQ[$CellContext`fp$$], $CellContext`fp$$ != {}], \ $CellContext`fp$$ = First[$CellContext`fp$$], Unset[$CellContext`fp$$]]; If[ And[ ListQ[$CellContext`fc$$], $CellContext`fc$$ != {}], \ $CellContext`fc$$ = First[$CellContext`fc$$], Unset[$CellContext`fc$$]]; If[ And[ ListQ[$CellContext`fs$$], $CellContext`fs$$ != {}], \ $CellContext`fs$$ = First[$CellContext`fs$$], Unset[$CellContext`fs$$]]; If[ And[ ListQ[$CellContext`fg$$], $CellContext`fg$$ != {}], \ $CellContext`fg$$ = First[$CellContext`fg$$], Unset[$CellContext`fg$$]]; If[ And[ ListQ[$CellContext`fr$$], $CellContext`fr$$ != {}], \ $CellContext`fr$$ = First[$CellContext`fr$$], Unset[$CellContext`fr$$]]); $CellContext`switchFilter := If[$CellContext`bAND$$ == 1, $CellContext`ifNum, $CellContext`ifLen]; \ $CellContext`clearFilter := If[$CellContext`bAND$$ == 1, $CellContext`setFlt, $CellContext`unsetFlt]; \ $CellContext`e8Filter[ Pattern[$CellContext`f, Blank[List]]] := Sum[2^Part[$CellContext`bOrd, $CellContext`i] Part[$CellContext`f, $CellContext`i], {$CellContext`i, 1, Length[$CellContext`f]}]; $CellContext`doFilter := Module[{$CellContext`runFilter$, $CellContext`bTest$, \ $CellContext`bCont$, $CellContext`bMatch$}, $CellContext`runFilter$[ Pattern[$CellContext`i$, Blank[]]] := (If[ And[$CellContext`bCont$, Length[$CellContext`fr$$] > 0], Map[If[ Or[# == 0, # == $CellContext`pRow[$CellContext`i$]], \ $CellContext`bMatch$ = True, If[$CellContext`bAND$$ == 2, $CellContext`bMatch$ = False; $CellContext`bCont$ = False]]& , $CellContext`fr$$]]; Map[If[ And[$CellContext`bCont$, Length[ Part[$CellContext`filterList, #]] > 0], Do[$CellContext`bTest$ = BitAnd[ $CellContext`pBit[$CellContext`i$], $CellContext`e8Filter[ ReplacePart[ Array[0& , Length[ Most[$CellContext`filterList]]], # -> If[# < 3, 1, 3]]]]; If[ Or[$CellContext`bTest$ == Part[$CellContext`filterList, #, $CellContext`j] == 0, And[$CellContext`bTest$ > 0, BitXor[$CellContext`bTest$, $CellContext`e8Filter[ ReplacePart[ Array[0& , Length[ Most[$CellContext`filterList]]], # -> Part[$CellContext`filterList, #, $CellContext`j]]]] == 0]], $CellContext`bMatch$ = True, If[$CellContext`bAND$$ == 2, $CellContext`bMatch$ = False; $CellContext`bCont$ = False]], {$CellContext`j, Length[ Part[$CellContext`filterList, #]]}]]& , Range[ Length[ Most[$CellContext`filterList]]]]); If[$CellContext`bAND$$ == 2, $CellContext`ifNum]; $CellContext`fltrdSubPlot$$ = {}; Map[If[Part[$CellContext`dispArr$$, #] == "y", AppendTo[$CellContext`fltrdSubPlot$$, #]]& , Range[$CellContext`le8]]; Map[($CellContext`bMatch$ = False; $CellContext`bCont$ = True; If[Sum[ Length[ Part[$CellContext`filterList, $CellContext`k]], \ {$CellContext`k, 1, Length[$CellContext`filterList]}] > 0, $CellContext`runFilter$[#], $CellContext`bMatch$ = True]; If[ And[$CellContext`bMatch$, Part[$CellContext`dispArr$$, #] == "?"], AppendTo[$CellContext`fltrdSubPlot$$, #]])& , Part[$CellContext`pls, $CellContext`position[$CellContext`plNames, \ $CellContext`pListName$$]]]; If[$CellContext`bAND$$ == 2, $CellContext`ifLen]]; $CellContext`dln[ Pattern[$CellContext`l$, Blank[]]] := Map[$CellContext`position[ Part[$CellContext`dl, $CellContext`ds$$], #]& , \ $CellContext`l$]; $CellContext`dls[ Pattern[$CellContext`l$, Blank[]]] := Part[$CellContext`dl, $CellContext`ds$$, $CellContext`l$]; \ $CellContext`dlXn := $CellContext`dln[$CellContext`dlXs$$]; $CellContext`dlYn := \ $CellContext`dln[$CellContext`dlYs$$]; $CellContext`dlZn := \ $CellContext`dln[$CellContext`dlZs$$]; $CellContext`rot\[Theta]List[ Pattern[$CellContext`\[Theta], Blank[List]], Pattern[$CellContext`hp, Blank[List]]] := Dot[ $CellContext`rot\[Theta][ Part[$CellContext`\[Theta], 3], Part[$CellContext`hp, 3]], $CellContext`rot\[Theta][ Part[$CellContext`\[Theta], 2], Part[$CellContext`hp, 2]], $CellContext`rot\[Theta][ Part[$CellContext`\[Theta], 1], Part[$CellContext`hp, 1]]]; $CellContext`rotXY[ Pattern[$CellContext`\[Theta], Blank[]]] := $CellContext`rot\[Theta][$CellContext`\[Theta], { $CellContext`dla[$CellContext`dlXn], $CellContext`dla[$CellContext`dlYn]}]; $CellContext`rotYZ[ Pattern[$CellContext`\[Theta], Blank[]]] := $CellContext`rot\[Theta][$CellContext`\[Theta], { $CellContext`dla[$CellContext`dlYn], $CellContext`dla[$CellContext`dlZn]}]; $CellContext`rotZX[ Pattern[$CellContext`\[Theta], Blank[]]] := $CellContext`rot\[Theta][$CellContext`\[Theta], { $CellContext`dla[$CellContext`dlZn], $CellContext`dla[$CellContext`dlXn]}]; $CellContext`rotXYZ[ Pattern[$CellContext`\[Theta]$, Blank[ List]]] := \ $CellContext`rot\[Theta]List[$CellContext`\[Theta]$, {{ $CellContext`dla[{$CellContext`dimTrim$$}], $CellContext`dla[ $CellContext`dln[$CellContext`dlXs$$]]}, { $CellContext`dla[{$CellContext`dimTrim$$}], $CellContext`dla[ $CellContext`dln[$CellContext`dlYs$$]]}, { $CellContext`dla[{$CellContext`dimTrim$$}], $CellContext`dla[ $CellContext`dln[$CellContext`dlZs$$]]}}]; \ $CellContext`nDRots[ Pattern[$CellContext`\[Theta], Blank[]]] := {{$CellContext`\[Theta], 0, 0}, {$CellContext`\[Theta], $CellContext`\[Theta]/2, 0}, {$CellContext`\[Theta], $CellContext`\[Theta]/ 2, $CellContext`\[Theta]/4}}; $CellContext`nDRot[ Pattern[$CellContext`\[Theta], Blank[]]] := Part[ $CellContext`nDRots[$CellContext`\[Theta]], 1]; $CellContext`initial := {$CellContext`HI, $CellContext`VI, \ $CellContext`ZI}; $CellContext`final := {$CellContext`HF, $CellContext`VF, \ $CellContext`ZF}; $CellContext`setIFpath := ($CellContext`HI = \ $CellContext`dla[$CellContext`dlXn]; $CellContext`VI = \ $CellContext`dla[$CellContext`dlYn]; $CellContext`ZI = \ $CellContext`dla[$CellContext`dlZn]; $CellContext`HF = Reverse[$CellContext`HI]; $CellContext`VF = Reverse[$CellContext`VI]; $CellContext`ZF = Reverse[$CellContext`ZI]; {$CellContext`iPath, \ $CellContext`fPath} = {$CellContext`initial, $CellContext`ptCds} + If[$CellContext`pthPtCds$$ == "Identity", 0, {-$CellContext`ptCds, 0}]); $CellContext`setPTo[ Pattern[$CellContext`\[Theta]$, Blank[]]] := ($CellContext`H$$ = Dot[ $CellContext`rotXY[$CellContext`\[Theta]$], Part[$CellContext`fPath, 1]]; $CellContext`V$$ = Dot[ $CellContext`rotYZ[$CellContext`\[Theta]$], Part[$CellContext`fPath, 2]]; $CellContext`Z$$ = Dot[ $CellContext`rotZX[$CellContext`\[Theta]$], Part[$CellContext`fPath, 3]]); $CellContext`setPTt[ Pattern[$CellContext`\[Theta]$, Blank[]]] := ($CellContext`H$$ = Part[$CellContext`fPath, 1]; $CellContext`V$$ = Cos[$CellContext`\[Theta]$] Part[$CellContext`fPath, 2] + Sin[$CellContext`\[Theta]$] Part[$CellContext`fPath, 3]; $CellContext`Z$$ = Part[$CellContext`fPath, 3]); $CellContext`eFct[ Pattern[$CellContext`in$, Blank[]]] := Min[$CellContext`minEdgeCnt, Floor[ If[$CellContext`in$ == $CellContext`eLim$$ - 1, $CellContext`minEdgeCnt, If[$CellContext`in$ == $CellContext`eLim$$, \ $CellContext`specialFct, If[$CellContext`in$ < $CellContext`eLim$$/ 3, $CellContext`in$, $CellContext`minEdgeCnt If[$CellContext`in$ < $CellContext`eLim$$ (2/ 3), $CellContext`in$/$CellContext`eLim$$ - 1/ 3, ((3/2) ($CellContext`in$/$CellContext`eLim$$) - 1/ 2)^($CellContext`in$/$CellContext`eLim$$)]]]]]]; \ $CellContext`norm[ Pattern[$CellContext`e, Blank[]]] := Norm[ N[ $CellContext`line2[ "verts", $CellContext`e]]]; $CellContext`elineSort[ Pattern[$CellContext`type$, Blank[]]] := SortBy[$CellContext`elines$$, If[$CellContext`type$ == "Ascending", $CellContext`norm[#], 1/($CellContext`chop + $CellContext`norm[#])]& ]; \ $CellContext`maxEdge := Max[ Map[$CellContext`norm, $CellContext`elines$$]]; \ $CellContext`doEdgeList[ Pattern[$CellContext`in$, Blank[]]] := Module[{$CellContext`strt$, $CellContext`end$}, Do[If[$CellContext`eSteps$$ > 1, $CellContext`end$ = Ceiling[$CellContext`minEdgeCnt \ ($CellContext`j1/$CellContext`eFct[$CellContext`eSteps$$])]; \ $CellContext`strt$ = Max[1, $CellContext`end$ - \ $CellContext`eFct[$CellContext`eWnd$$]]; $CellContext`elines$$ = Part[$CellContext`eSort$$, Span[$CellContext`strt$, $CellContext`end$]]]; \ $CellContext`processOut[$CellContext`eFct[$CellContext`eSteps$$] \ ($CellContext`in$ - 1) + $CellContext`j1], {$CellContext`j1, $CellContext`eFct[$CellContext`eSteps$$]}]; \ $CellContext`eSort$$ = {}]; $CellContext`processImage[ Pattern[$CellContext`in$, Blank[]]] := Module[{$CellContext`i$}, If[ And[$CellContext`showEdges$$, Or[$CellContext`eSteps$$ > 1, $CellContext`anim8EdgeList$$]], $CellContext`i$ = 1; Map[{$CellContext`elines$$ = $CellContext`eLines[#]; \ $CellContext`edgeMag$$ = Max[$CellContext`chop, $CellContext`maxEdge]; \ $CellContext`elines$$ = ($CellContext`eSort$$ = $CellContext`elineSort[ "Ascending"]); $CellContext`doEdgeList[ If[$CellContext`anim8EdgeList$$, Length[ Most[$CellContext`edgeList$$]], 1] ($CellContext`in$ - 1) + Increment[$CellContext`i$]]}& , If[$CellContext`anim8EdgeList$$, Most[$CellContext`edgeList$$], $CellContext`edgeVals$$]], $CellContext`processOut[$CellContext`in$]]]; \ $CellContext`doAnim8 := Module[{$CellContext`HSav$ = $CellContext`H$$, \ $CellContext`VSav$ = $CellContext`V$$, $CellContext`ZSav$ = $CellContext`Z$$, \ $CellContext`elineSav$ = $CellContext`elines$$, $CellContext`edgeValsSav$ = \ $CellContext`edgeVals$$}, $CellContext`loop = {}; $CellContext`setIFpath; Map[{$CellContext`\[Theta] = 2 Pi (# $CellContext`steps$$^(-1)/2); Switch[$CellContext`pthRot$$, "Spin", $CellContext`lastViewPoint$$ = { Cos[$CellContext`\[Theta]], Sin[$CellContext`\[Theta]], 0.001} Subscript[$CellContext`range$$, $CellContext`scaled], "Trans", $CellContext`setPTt[$CellContext`\[Theta]], "Trans&Rot", $CellContext`setPTo[$CellContext`\[Theta]]]; \ $CellContext`processImage[#]}& , Range[$CellContext`steps$$]]; If[ And[$CellContext`loop != {}, Not[$CellContext`fileOnly$$]], $CellContext`out = ListAnimate[$CellContext`loop, DefaultDuration -> 3, AnimationRunning -> False]]; $CellContext`H$$ = $CellContext`HSav$; \ $CellContext`V$$ = $CellContext`VSav$; $CellContext`Z$$ = $CellContext`ZSav$; \ $CellContext`elines$$ = $CellContext`elineSav$; $CellContext`edgeVals$$ = \ $CellContext`edgeValsSav$]; $CellContext`listToPos[ Pattern[$CellContext`pLst, Blank[List]], Pattern[$CellContext`vLst, Blank[List]]] := Module[{$CellContext`i}, Map[Map[Apply[$CellContext`position[$CellContext`pLst, Part[$CellContext`vLst, #, #2]]& , {$CellContext`i, #}]& , Range[ Length[ Part[$CellContext`vLst, $CellContext`i = #]]]]& , Range[ Length[$CellContext`vLst]]]]; $CellContext`line2["verts", Pattern[$CellContext`e$, Blank[]]] := {$CellContext`edge1 = $CellContext`posTbl[ Part[$CellContext`verts$$, Part[$CellContext`e$, 1]]], $CellContext`edge2 = $CellContext`posTbl[ Part[$CellContext`verts$$, Part[$CellContext`e$, 2]]]}; $CellContext`line2["fullVerts", Pattern[$CellContext`e$, Blank[]]] := {$CellContext`edge1 = $CellContext`posTbl[ Part[$CellContext`fullVerts$$, Part[$CellContext`e$, 1]]], $CellContext`edge2 = $CellContext`posTbl[ Part[$CellContext`fullVerts$$, Part[$CellContext`e$, 2]]]}; $CellContext`line3["verts", Pattern[$CellContext`e$, Blank[]]] := Join[ $CellContext`line2[ "verts", $CellContext`e$], {$CellContext`edge3 = \ $CellContext`posTbl[ Part[$CellContext`verts$$, Part[$CellContext`e$, 3]]]}]; $CellContext`line3[ "fullVerts", Pattern[$CellContext`e$, Blank[]]] := Join[ $CellContext`line2[ "fullVerts", $CellContext`e$], {$CellContext`edge3 = \ $CellContext`posTbl[ Part[$CellContext`fullVerts$$, Part[$CellContext`e$, 3]]]}]; $CellContext`getVContent[ Pattern[$CellContext`v$, Blank[]]] := Select[$CellContext`elines$$, Or[$CellContext`v$ == Part[#, 1], $CellContext`v$ == Part[#, 2]]& ]; $CellContext`getU[ Pattern[$CellContext`v, Blank[]]] := Module[{$CellContext`uLst}, Delete[$CellContext`uLst = Union[ Flatten[ $CellContext`getVContent[$CellContext`v]]], $CellContext`position[$CellContext`uLst, $CellContext`v]]]; \ $CellContext`nFaces[ Pattern[$CellContext`vLst, Blank[List]]] := Module[{$CellContext`nlv, $CellContext`np, $CellContext`nlst = \ {}}, $CellContext`nlv = Map[$CellContext`getU, $CellContext`vLst]; Map[Do[ If[$CellContext`i != \ $CellContext`position[$CellContext`nlv, #], $CellContext`np = Position[ Part[$CellContext`nlv, $CellContext`i], Part[#, $CellContext`j]]; If[$CellContext`np != {}, AppendTo[$CellContext`nlst, Part[#, $CellContext`j]]]], {$CellContext`i, Length[$CellContext`nlv]}, {$CellContext`j, Length[#]}]& , $CellContext`nlv]; Map[Join[$CellContext`vLst, {#}]& , Union[$CellContext`nlst]]]; $CellContext`polySurfaces := Map[If[$CellContext`p3D$$ == Part[$CellContext`p3DList, 1], { Opacity[0.5], Pink, Polygon[ $CellContext`line3["verts", #]]}, Polygon[ $CellContext`line3["verts", #]]]& , $CellContext`noDups[ Flatten[ Map[$CellContext`nFaces, Sort[$CellContext`elines$$]], 1]]]; $CellContext`e8Surface[ Pattern[$CellContext`p$, Blank[]]] := Inset[ Part[ Flatten[ If[$CellContext`p3D$$ == Part[$CellContext`p3DList, 1], $CellContext`orb2D, $CellContext`orb3Ds]], $CellContext`position[$CellContext`graphicList, $CellContext`getNLM[ $CellContext`get120[$CellContext`p$]]]], $CellContext`posTbl[ $CellContext`dsGet[$CellContext`p$]], {0, 0}, If[$CellContext`p3D$$ == Part[$CellContext`p3DList, 1], 1/200, 6] Part[ Subscript[$CellContext`XY$$, $CellContext`scaled], 3] Part[ ReleaseHold[ $CellContext`pShpSze[$CellContext`p$]], 2]]; $CellContext`surfaces := Map[$CellContext`e8Surface, $CellContext`fltrdSubPlot$$]; \ $CellContext`rectifyEdges := ($CellContext`rectNodes$$ = Apply[Subtract, Subsets[$CellContext`rectNodes$$, {2}], { 1}]); $CellContext`rectifyParticles := \ ($CellContext`rectNodes$$ = Map[($CellContext`line2[ "verts", #]; ($CellContext`edge1 + $CellContext`edge2)/ 2)& , $CellContext`elines$$]; Map[$CellContext`rectifyEdges& , Range[$CellContext`rectification$$ - 1]]; Map[{ If[$CellContext`vOverlapColor$$, $CellContext`getColor[ $CellContext`count[$CellContext`rectNodes$$, #]], Black], $CellContext`poly[{$CellContext`cir, 1/2}, #, Subscript[$CellContext`scale$$, $CellContext`scaled], \ $CellContext`plDims]}& , $CellContext`rectNodes$$]); $CellContext`tLines := Module[{$CellContext`chkTri$, $CellContext`rPt$, \ $CellContext`rPtt$, $CellContext`tmpPos1$, $CellContext`tmpPos2$}, \ $CellContext`chkTri$[ Pattern[$CellContext`isFirst$, Blank[]], Pattern[$CellContext`p$, Blank[]]] := Map[If[Position[$CellContext`tT$$, Part[$CellContext`triList, #]] != {}, FullSimplify[ Dot[ If[$CellContext`isFirst$, IdentityMatrix[$CellContext`dims], Part[$CellContext`triListExp, #]], Part[$CellContext`triListExp, #], $CellContext`p$]], First[$CellContext`fullVerts$$]]& , Range[ Length[$CellContext`triList]]]; If[$CellContext`fltrdSubPlot$$ != {}, $CellContext`fullVerts$$ = Map[$CellContext`dsGet, $CellContext`fltrdSubPlot$$]; \ $CellContext`rPt$ = Flatten[ Map[$CellContext`chkTri$[ True, #]& , $CellContext`fullVerts$$], 1]; $CellContext`rPtt$ = Flatten[ Map[$CellContext`chkTri$[ False, #]& , $CellContext`fullVerts$$], 1]; $CellContext`noDups[ $CellContext`noNull[ Flatten[ Map[Table[{#, $CellContext`position[$CellContext`fullVerts$$, Part[$CellContext`rPt$, Length[$CellContext`triList] (# - 1) + $CellContext`i]], $CellContext`position[$CellContext`fullVerts$$, Part[$CellContext`rPtt$, Length[$CellContext`triList] (# - 1) + $CellContext`i]]}, {$CellContext`i, Length[$CellContext`triList]}]& , Range[ Length[$CellContext`fullVerts$$]]], 1]]], $CellContext`fullVerts$$ = {}]]; $CellContext`pLines[ Pattern[$CellContext`pList$, Blank[]]] := Map[Module[{$CellContext`nl$ = {}, $CellContext`vl$}, \ $CellContext`vLines[{#}]; $CellContext`vl$ = DeleteCases[ Union[ Map[Part[$CellContext`fltrdSubPlot$$, #]& , Flatten[$CellContext`vlines$$]]], #]; Do[ If[$CellContext`pE8[ Part[$CellContext`vl$, $CellContext`i]] + $CellContext`pE8[ Part[$CellContext`vl$, $CellContext`j]] == \ $CellContext`pE8[#], AppendTo[$CellContext`nl$, {#, Part[$CellContext`vl$, $CellContext`i], Part[$CellContext`vl$, $CellContext`j]}]], \ {$CellContext`i, $CellContext`j + 1, Length[$CellContext`vl$]}, {$CellContext`j, Length[$CellContext`vl$]}]; $CellContext`plines$$ = Join[$CellContext`plines$$, $CellContext`noDups[$CellContext`nl$]]]& , \ $CellContext`pList$]; $CellContext`vertexTally := Module[{$CellContext`tly2$}, $CellContext`tly2$ = Sort[ Tally[ Part[ Tally[ N[ Round[ If[$CellContext`rectification$$ == 0, $CellContext`pPList, $CellContext`rectNodes$$], \ $CellContext`cntChop]]], All, 2]]]; $CellContext`tly1 = Map[{ Part[#, 1], Part[#, 1] Part[#, 2]}& , $CellContext`tly2$]]; $CellContext`vLineTally := \ {}; $CellContext`vLines[ Pattern[$CellContext`pList$, Blank[]]] := Module[{$CellContext`allAngles$, $CellContext`setAllColors$, \ $CellContext`getAngle$, $CellContext`vAngles$, $CellContext`ltp$, \ $CellContext`newVlines$, $CellContext`newOverlaps$, $CellContext`newVcolors$, \ $CellContext`setVcolor$, $CellContext`vls$, $CellContext`jj$, \ $CellContext`sav$, $CellContext`new$, $CellContext`lalp$, \ $CellContext`allPos$, $CellContext`nls$}, $CellContext`setAllColors$ := Do[$CellContext`allPos$ = Position[$CellContext`allAngles$, Part[$CellContext`vAngles$, $CellContext`k], 1, Heads -> False]; $CellContext`sav$ = Flatten[ Delete[$CellContext`allPos$, Position[$CellContext`allPos$, { Part[$CellContext`nls$, $CellContext`k]} 1, Heads -> False]]]; $CellContext`new$ = {}; $CellContext`new$ = Flatten[ AppendTo[$CellContext`new$, Map[Permutations[{ Part[$CellContext`nls$, $CellContext`k], #}]& , \ $CellContext`sav$]], 2]; $CellContext`lalp$ = Length[ Flatten[ Map[ Position[$CellContext`elines$$, #, 1, Heads -> False]& , $CellContext`new$]]]; Part[$CellContext`newVcolors$, $CellContext`k] = Part[$CellContext`newVcolors$, $CellContext`k] + \ $CellContext`lalp$, {$CellContext`k, Range[ Length[$CellContext`vAngles$]]}]; $CellContext`setVcolor$ := Map[(Part[$CellContext`newVcolors$, First[#]] = PreIncrement[$CellContext`jj$])& , $CellContext`vls$]; \ $CellContext`getAngle$[ Pattern[$CellContext`vLst, Blank[List]]] := N[ Round[ Normalize[Part[ $CellContext`line2["verts", $CellContext`vLst], 2] - First[ $CellContext`line2[ "verts", $CellContext`vLst]]], $CellContext`chop]]; Map[($CellContext`ltp$ = $CellContext`first[ Flatten[ $CellContext`listToPos[$CellContext`fltrdSubPlot$$, \ {{#}}]]]; $CellContext`ltps$$ = AppendTo[$CellContext`ltps$$, #]; $CellContext`vlines$$ = Join[$CellContext`vlines$$, $CellContext`newVlines$ = \ $CellContext`getVContent[$CellContext`ltp$]]; $CellContext`newOverlaps$ = \ ($CellContext`newVcolors$ = Array[1& , { Length[$CellContext`newVlines$]}]); $CellContext`nls$ = Map[$CellContext`first[ Delete[#, $CellContext`position[#, $CellContext`ltp$]]]& , \ $CellContext`newVlines$]; $CellContext`vAngles$ = Map[$CellContext`getAngle$[{$CellContext`ltp$, #}]& , \ $CellContext`nls$]; $CellContext`allAngles$ = Map[$CellContext`getAngle$[{$CellContext`ltp$, #}]& , Range[ Length[$CellContext`fltrdSubPlot$$]]]; Map[(Part[$CellContext`newOverlaps$, #] = Length[$CellContext`vls$ = Position[$CellContext`vAngles$, Part[$CellContext`vAngles$, #], 1, Heads -> False]]; $CellContext`jj$ = 0; $CellContext`setVcolor$)& , Range[ Length[$CellContext`vAngles$]]]; \ $CellContext`setAllColors$; $CellContext`vLineColors$$ = Flatten[ Join[$CellContext`vLineColors$$, \ $CellContext`newVcolors$]]; $CellContext`vLineTally)& , $CellContext`pList$]]; \ $CellContext`minEdgeCnt := Min[{ If[Length[$CellContext`eSort$$] == 0, Infinity, Length[$CellContext`eSort$$]], If[Min[ Part[$CellContext`edgeVals$$, All, 2]] == 0, Infinity, Min[ Part[$CellContext`edgeVals$$, All, 2]]]}]; $CellContext`getEdges := Module[{$CellContext`eVsubs$, $CellContext`eValFull$, \ $CellContext`eValCnt$, $CellContext`fullEdgeCount$, $CellContext`edgeCount$, \ $CellContext`fltrInnerVerts$, $CellContext`stepSav$ = $CellContext`steps$$, \ $CellContext`perspectiveSav$ = $CellContext`perspective$$, $CellContext`eVl$, \ $CellContext`eVp$, $CellContext`eVC$}, $CellContext`eVsubs$[ Pattern[$CellContext`v, Blank[]]] := Subsets[ Range[ Length[$CellContext`v]], {2}]; $CellContext`eValFull$[ Pattern[$CellContext`verts$, Blank[]], Pattern[$CellContext`eVs$, Blank[]]] := Map[FullSimplify[ ToRadicals[ Sqrt[Norm[ FullSimplify[ Apply[Subtract, Part[$CellContext`verts$, #, Span[ 1, $CellContext`dimTrim$$]]]]]^2]]]& , $CellContext`eVs$]; \ $CellContext`eValCnt$[ Pattern[$CellContext`eValFull, Blank[]], Pattern[$CellContext`eVal, Blank[]]] := Map[Length[ Position[$CellContext`eValFull, #, 1, Heads -> False]]& , $CellContext`eVal]; $CellContext`fullEdgeCount$[ Pattern[$CellContext`n, Blank[]]] := Binomial[$CellContext`n, 2]; $CellContext`edgeCount$[ Pattern[$CellContext`eVC$, Blank[]]] := Min[ $CellContext`fullEdgeCount$[ Length[$CellContext`verts$$]], Total[ Map[#& , $CellContext`eVC$]]]; \ $CellContext`fltrInnerVerts$ := Module[{$CellContext`maxVert$}, $CellContext`maxVert$ = Max[ Map[Norm, Map[$CellContext`posTbl, $CellContext`fullVerts$$]]]; \ $CellContext`verts$$ = Select[$CellContext`fullVerts$$, Norm[ $CellContext`posTbl[#]] >= $CellContext`innerMag$$ \ $CellContext`maxVert$& ]]; $CellContext`perspective$$ = False; $CellContext`steps$$ = 1; $CellContext`fltrInnerVerts$; $CellContext`edgeVals$$ = { If[ Length[$CellContext`verts$$] > 1, $CellContext`eVs$$ = \ $CellContext`eVsubs$[$CellContext`verts$$]; $CellContext`eVF$$ = \ $CellContext`eValFull$[$CellContext`verts$$, $CellContext`eVs$$]; \ $CellContext`eVl$ = Sort[ $CellContext`noDups[$CellContext`eVF$$]]; \ $CellContext`eVC$ = $CellContext`eValCnt$[$CellContext`eVF$$, \ $CellContext`eVl$]; AppendTo[$CellContext`eVC$, $CellContext`edgeCount$[$CellContext`eVC$]]; AppendTo[$CellContext`eVl$, "All"]; $CellContext`edgeList$$ = Map[{ Part[$CellContext`eVl$, #], Part[$CellContext`eVC$, #]}& , Range[ Length[$CellContext`eVl$]]]; If[ And[$CellContext`edgeVals$$ != {{0, 0}}, ($CellContext`eVp$ = Position[$CellContext`eVl$, Part[$CellContext`edgeVals$$, 1, 1], 1, Heads -> False]) != {}], Part[$CellContext`edgeList$$, $CellContext`first[ Flatten[$CellContext`eVp$]]], First[$CellContext`edgeList$$]], $CellContext`edgeList$$ = \ {{0, 0}, {"All", 0}}; First[$CellContext`edgeList$$]]}; \ $CellContext`perspective$$ = $CellContext`perspectiveSav$; \ $CellContext`steps$$ = $CellContext`stepSav$]; $CellContext`eLines[ Pattern[$CellContext`edgeVal$, Blank[]]] := If[N[ First[$CellContext`edgeVal$]] == "All", Flatten[ Map[$CellContext`eLines, Most[$CellContext`edgeList$$]], 1], If[Length[$CellContext`verts$$] > 1, Part[$CellContext`eVs$$, Flatten[ Position[$CellContext`eVF$$, First[$CellContext`edgeVal$], 1, Heads -> False]]], {}]]; $CellContext`edgeColor[ Pattern[$CellContext`e$, Blank[]]] := If[$CellContext`eColorPos$$, If[ And[$CellContext`eGrad$$ > 0, $CellContext`eGrad$$ < 51], ColorData[ $CellContext`gradName[$CellContext`eGrad$$], \ $CellContext`norm[$CellContext`e$]/$CellContext`edgeMag$$], $CellContext`getColor[$CellContext`eGrad$$, Ceiling[ Length[$CellContext`oldColors] \ ($CellContext`norm[$CellContext`e$]/$CellContext`edgeMag$$)]]], If[ And[$CellContext`eGrad$$ > 0, $CellContext`eGrad$$ < 51], ColorData[ $CellContext`gradName[$CellContext`eGrad$$], \ $CellContext`position[$CellContext`elines$$, $CellContext`e$]/ Length[$CellContext`elines$$]], $CellContext`getColor[$CellContext`eGrad$$, $CellContext`position[$CellContext`elines$$, \ $CellContext`e$]]]]; $CellContext`edgeLines := Map[If[ Or[$CellContext`plDims == 2, Not[$CellContext`artPrint$$], Not[$CellContext`cylOK]], { Thickness[$CellContext`thck], $CellContext`edgeColor[#], Line[ $CellContext`line2["verts", #]]}, { Specularity[White, $CellContext`specularity], $CellContext`edgeColor[#], Table[ Cylinder[ $CellContext`line2[ "verts", #], $CellContext`cylR$$ (1 - $CellContext`i/ 3)], {$CellContext`i, 0, $CellContext`numCyls}]}]& , $CellContext`elines$$]; \ $CellContext`physEdges := If[$CellContext`plines$$ == {}, $CellContext`nullPt, Map[($CellContext`line3["fullVerts", #]; If[ And[$CellContext`plDims == 3, $CellContext`artPrint$$, $CellContext`cylOK], Table[{{ Specularity[White, $CellContext`specularity], Opacity[1/2], $CellContext`pColor[$CellContext`pGrad$$, "r", "m"], Cylinder[{$CellContext`edge1, $CellContext`edge2}, \ $CellContext`cylR$$ (3 - $CellContext`i)], Cylinder[{$CellContext`edge1, $CellContext`edge3}, \ $CellContext`cylR$$ (3 - $CellContext`i)]}, { $CellContext`pColor[$CellContext`pGrad$$, "g", "m"], Cylinder[{$CellContext`edge2, $CellContext`edge3}, \ $CellContext`cylR$$ (3 - $CellContext`i)]}}, {$CellContext`i, 0, $CellContext`numCyls}], {{ Thickness[2 $CellContext`thck], Opacity[1/2], $CellContext`pColor[$CellContext`pGrad$$, "r", "m"], Line[{$CellContext`edge1, $CellContext`edge2}], Line[{$CellContext`edge1, $CellContext`edge3}]}, { Thickness[3 $CellContext`thck], $CellContext`pColor[$CellContext`pGrad$$, "g", "m"], Line[{$CellContext`edge2, $CellContext`edge3}]}}])& , $CellContext`noNull[ $CellContext`listToPos[$CellContext`fltrdSubPlot$$, \ $CellContext`plines$$]]]]; $CellContext`vertEdges := Map[If[ And[$CellContext`plDims == 3, $CellContext`artPrint$$, $CellContext`cylOK], { Specularity[White, $CellContext`specularity], Opacity[1/2], $CellContext`getColor[3 Part[$CellContext`vLineColors$$, #]], Table[ Cylinder[ $CellContext`line2["verts", Part[$CellContext`vlines$$, #]], $CellContext`cylR$$ ( 1 - $CellContext`i/3)], {$CellContext`i, 0, $CellContext`numCyls}]}, { Thickness[(Max[$CellContext`vLineColors$$] + 1 - Part[$CellContext`vLineColors$$, #]) 1 $CellContext`thck], Opacity[1/2], $CellContext`getColor[3 Part[$CellContext`vLineColors$$, #]], Line[ $CellContext`line2["verts", Part[$CellContext`vlines$$, #]]]}]& , Range[ Length[$CellContext`vlines$$]]]; $CellContext`perim := { Opacity[1/10], If[$CellContext`dsName$$ == First[$CellContext`dsNames], If[$CellContext`plDims == 2, Rectangle[], Cuboid[]], If[$CellContext`plDims == 2, Disk[$CellContext`dimZeros, 1.], Sphere[$CellContext`dimZeros, 1.]]]}; $CellContext`pVecs := Map[{ Thickness[$CellContext`thck2], $CellContext`pColor[$CellContext`pGrad$$, "w", "m"], Line[{$CellContext`dimZeros, $CellContext`pPos[#]}]}& , $CellContext`fltrdSubPlot$$]; \ $CellContext`pLabels := Map[{ Tooltip[ Text[ Style[ Column[{#, If[$CellContext`physics$$, $CellContext`pLbl, \ $CellContext`pE8][#]}], Medium, Bold], $CellContext`pPos[#]], Text[ Grid[{{ $CellContext`pDisp[#]}, { $CellContext`pToolTipTxt[#]}}]]]}& , \ $CellContext`fltrdSubPlot$$]; $CellContext`pLocs := Map[{ Text[ Style[ StringJoin[ ToString[ $CellContext`dsGet[#], FormatType -> StandardForm], "->", ToString[ $CellContext`pPos[#], FormatType -> StandardForm]], Medium], $CellContext`pPos[#], (-2) $CellContext`dlPtDef]}& , \ $CellContext`fltrdSubPlot$$]; $CellContext`pMassLife := Map[{ Text[ $CellContext`tipTxtMass[#], $CellContext`pPos[#], 5 $CellContext`dlPtDef], Text[ $CellContext`tipTxtLife[#], $CellContext`pPos[#], 3 $CellContext`dlPtDef]}& , $CellContext`fltrdSubPlot$$]; \ $CellContext`particles := Map[If[$CellContext`useDimLocs$$, Translate[$CellContext`zeroPt, $CellContext`pPos[#]], If[ And[$CellContext`plDims == 3, $CellContext`artPrint$$], { If[$CellContext`physics$$, $CellContext`pColor[$CellContext`pGrad$$, $CellContext`pColr[#], $CellContext`pShde[#]], If[$CellContext`vOverlapColor$$, $CellContext`getColor[ $CellContext`count[$CellContext`pPList, $CellContext`pPos[#]]], If[ MemberQ[ $CellContext`noDups[ Flatten[$CellContext`vlines$$]], $CellContext`first[ Flatten[ $CellContext`listToPos[$CellContext`fltrdSubPlot$$, \ {{#}}]]]], If[ MemberQ[$CellContext`ltps$$, #], Green, Red], Black]]], $CellContext`poly[ If[$CellContext`physics$$, $CellContext`pShpSze[#], {$CellContext`cir, 1/2}], $CellContext`pPos[#], Subscript[$CellContext`scale$$, $CellContext`scaled], \ $CellContext`plDims]}, { EdgeForm[{Thin, $CellContext`pColor[$CellContext`pGrad$$, "w", "l"]}], Tooltip[{ If[$CellContext`physics$$, $CellContext`pColor[$CellContext`pGrad$$, $CellContext`pColr[#], $CellContext`pShde[#]], If[$CellContext`vOverlapColor$$, $CellContext`getColor[ $CellContext`count[$CellContext`pPList, $CellContext`pPos[#]]], If[ MemberQ[ $CellContext`noDups[ Flatten[$CellContext`vlines$$]], $CellContext`first[ Flatten[ $CellContext`listToPos[$CellContext`fltrdSubPlot$$, \ {{#}}]]]], If[ MemberQ[$CellContext`ltps$$, #], Green, Red], Black]]], $CellContext`poly[ If[$CellContext`physics$$, $CellContext`pShpSze[#], {$CellContext`cir, 1/2}], $CellContext`pPos[#], Subscript[$CellContext`scale$$, $CellContext`scaled], \ $CellContext`plDims]}, Text[ Grid[{{ $CellContext`pDisp[#]}, { $CellContext`pToolTipTxt[#]}}]]]}]]& , \ $CellContext`fltrdSubPlot$$]; $CellContext`cylCnt := If[$CellContext`showEdges$$, Length[$CellContext`elines$$], 0] + Length[$CellContext`tlines$$] + Length[$CellContext`plines$$] + Length[$CellContext`vlines$$]; $CellContext`opacityOK := If[$CellContext`cylCnt > $CellContext`cylBreakPnt, False, True]; $CellContext`cylOK := Or[$CellContext`opacityOK, $CellContext`forceCyl]; \ $CellContext`triLines := Map[($CellContext`line3["fullVerts", #]; If[ And[$CellContext`plDims == 3, $CellContext`artPrint$$, $CellContext`cylOK], Table[{ Specularity[White, $CellContext`specularity], Opacity[1/2], $CellContext`pColor[$CellContext`pGrad$$, "b", "m"], Cylinder[{$CellContext`edge1, $CellContext`edge2}, \ $CellContext`cylR$$ (1 - $CellContext`i/3)], Cylinder[{$CellContext`edge2, $CellContext`edge3}, \ $CellContext`cylR$$ (1 - $CellContext`i/3)], Cylinder[{$CellContext`edge3, $CellContext`edge1}, \ $CellContext`cylR$$ (1 - $CellContext`i/3)]}, {$CellContext`i, 0, $CellContext`numCyls}], { Thickness[$CellContext`thck2], Opacity[1/2], $CellContext`pColor[$CellContext`pGrad$$, "b", "m"], Line[{$CellContext`edge1, $CellContext`edge2}], Line[{$CellContext`edge2, $CellContext`edge3}], Line[{$CellContext`edge3, $CellContext`edge1}]}])& , \ $CellContext`tlines$$]; $CellContext`labels := Join[{ If[$CellContext`showAxes$$, Map[{{Dashed, Black, Line[$CellContext`zoomFct { Table[-Part[$CellContext`ptCds, $CellContext`j, #], \ {$CellContext`j, $CellContext`plDims}], Table[ Part[$CellContext`ptCds, $CellContext`j, #], \ {$CellContext`j, $CellContext`plDims}]}], Text[ Style[ Part[$CellContext`dl, $CellContext`ds$$, #], If[$CellContext`showPvecs$$, Large, Medium]], $CellContext`zoomFct Table[ Part[$CellContext`ptCds, $CellContext`k, #], \ {$CellContext`k, $CellContext`plDims}], $CellContext`dlPtDef]}, If[$CellContext`useDimLocs$$, With[{$CellContext`i$ = #}, Locator[ Dynamic[ Part[$CellContext`locPtCdArr$$, $CellContext`i$]]]], Translate[$CellContext`axesPt, Table[ Part[$CellContext`ptCds, $CellContext`j, #], \ {$CellContext`j, $CellContext`plDims}]]]}& , Range[$CellContext`dims]], {$CellContext`nullPt}]}]; \ $CellContext`callImage := Module[{$CellContext`graph$ = {$CellContext`nullPt}}, If[$CellContext`showPerim$$, AppendTo[$CellContext`graph$, $CellContext`perim]]; If[ And[$CellContext`showEdges$$, Length[$CellContext`elines$$] > 1, $CellContext`rectification$$ == 0], AppendTo[$CellContext`graph$, $CellContext`edgeLines]]; If[$CellContext`showPvecs$$, AppendTo[$CellContext`graph$, $CellContext`pVecs]]; If[$CellContext`ltps$$ != {}, AppendTo[$CellContext`graph$, If[$CellContext`physics$$, $CellContext`physEdges, \ $CellContext`vertEdges]]]; If[$CellContext`showPlocs$$, AppendTo[$CellContext`graph$, $CellContext`pLocs]]; If[$CellContext`showPmass$$, AppendTo[$CellContext`graph$, $CellContext`pMassLife]]; If[$CellContext`showPartVert$$, AppendTo[$CellContext`graph$, If[ And[$CellContext`vOverlapColor$$, Not[$CellContext`useDimLocs$$]], \ $CellContext`vertexTally]; If[$CellContext`rectification$$ > 0, $CellContext`rectifyParticles, \ $CellContext`particles]]]; If[$CellContext`showSurfaces$$, AppendTo[$CellContext`graph$, $CellContext`surfaces]]; If[$CellContext`tT$$ != {}, AppendTo[$CellContext`graph$, $CellContext`triLines]]; If[$CellContext`showPolySurfaces$$, AppendTo[$CellContext`graph$, $CellContext`polySurfaces]]; If[$CellContext`showPtext$$, AppendTo[$CellContext`graph$, $CellContext`pLabels]]; AppendTo[$CellContext`graph$, $CellContext`labels]; \ $CellContext`graph$]; $CellContext`viewPoint := $CellContext`lastViewPoint$$ + If[ And[$CellContext`pthRot$$ != "Spin", $CellContext`eSteps$$ == 1, $CellContext`steps$$ == 1], 0, If[ And[$CellContext`pthRot$$ == "Spin", $CellContext`centerSpin], \ -$CellContext`lastViewPoint$$, If[ And[$CellContext`eSteps$$ == 1, $CellContext`steps$$ == 1], Join[ Subscript[$CellContext`xyVwPnt$$, $CellContext`scaled], { Subscript[$CellContext`zVwPnt$$, $CellContext`scaled]}], 0]]]; $CellContext`viewCenter := {1, 1, 1}/2 + If[ And[$CellContext`pthRot$$ == "Spin", $CellContext`centerSpin], \ $CellContext`lastViewPoint$$/2, {0, 0, 0}]; $CellContext`viewAngle := If[$CellContext`centerSpin, 155 Degree, 45 Degree]; $CellContext`sphericalRegion := If[ And[$CellContext`pthRot$$ == "Spin", $CellContext`centerSpin], True, False]; $CellContext`axesLabel = { "X", "Y", "Z"}; $CellContext`axesEdge = { Automatic, Automatic, Automatic}; $CellContext`params := { Ticks -> $CellContext`tickRange, ImageSize -> $CellContext`imageSize}; $CellContext`param2D := Join[$CellContext`params, { PlotRange -> Part[$CellContext`plotRange, Span[1, 2]], Axes -> False, PlotRangeClipping -> False, AxesLabel -> Part[$CellContext`axesLabel, Span[1, 2]]}]; $CellContext`param3D := Join[$CellContext`params, { PlotRange -> $CellContext`plotRange, Boxed -> $CellContext`showAxes$$, Axes -> $CellContext`showAxes$$, AxesLabel -> $CellContext`axesLabel, AxesEdge -> $CellContext`axesEdge, FaceGrids -> $CellContext`faceGrids, FaceGridsStyle -> Directive[Gray, Dotted], AspectRatio -> 1, SphericalRegion -> $CellContext`sphericalRegion, ViewPoint -> $CellContext`viewPoint, ViewCenter -> $CellContext`viewCenter, ViewAngle -> $CellContext`viewAngle}]; \ $CellContext`findClicked[ Pattern[$CellContext`i$, Blank[]]] := Module[{$CellContext`nList$, $CellContext`clicked$, \ $CellContext`func$, $CellContext`pos$, $CellContext`np$, $CellContext`vl$}, \ $CellContext`clicked$ = $CellContext`position[$CellContext`nList$ = Map[$CellContext`pPos, Range[$CellContext`le8]], First[ Nearest[$CellContext`nList$, $CellContext`i$, 1]]]; $CellContext`vl$ = Union[ If[$CellContext`physics$$, Flatten[$CellContext`plines$$], Part[$CellContext`fltrdSubPlot$$, Flatten[$CellContext`vlines$$]]]]; $CellContext`np$ = \ $CellContext`first[ Flatten[ If[$CellContext`physics$$, Position[$CellContext`plines$$, $CellContext`clicked$], Position[$CellContext`vlines$$, $CellContext`first[ Flatten[ $CellContext`listToPos[$CellContext`fltrdSubPlot$$, \ {{$CellContext`clicked$}}]]]]]]]; If[ NumericQ[$CellContext`pos$ = \ $CellContext`position[$CellContext`vl$, $CellContext`clicked$]], If[$CellContext`physics$$, $CellContext`plines$$ = { Part[$CellContext`plines$$, $CellContext`np$]}, \ $CellContext`vlines$$ = { Part[$CellContext`vlines$$, $CellContext`np$]}], \ $CellContext`ltps$$ = {$CellContext`clicked$}]]; $CellContext`g2D := If[$CellContext`useDimLocs$$, Graphics[$CellContext`callImage, $CellContext`param2D], ClickPane[ Graphics[$CellContext`callImage, $CellContext`param2D], \ ($CellContext`findClicked[#]; $CellContext`refresh$$ = True)& ]]; $CellContext`g3D := Graphics3D[$CellContext`callImage, $CellContext`param3D]; \ $CellContext`tickRangeCalc := Table[$CellContext`i, {$CellContext`i, 0, 1, 1/$CellContext`tickNum$$}] Subscript[$CellContext`range$$, $CellContext`scaled]; \ $CellContext`tickRange := Map[Join[-$CellContext`tickRangeCalc, \ $CellContext`tickRangeCalc]& , Range[$CellContext`plDims]]; $CellContext`faceGrids := If[ And[$CellContext`showAxes$$, Not[$CellContext`artPrint$$]], {{{1, 0, 0}, Part[$CellContext`tickRange, Span[1, 2]]}, {{0, 1, 0}, Part[$CellContext`tickRange, Span[1, 2]]}, {{0, 0, 1}, Part[$CellContext`tickRange, Span[1, 2]]}}, None]; $CellContext`plotRange := Map[{Part[$CellContext`pt$$, #] - Subscript[$CellContext`range$$, $CellContext`scaled], Part[$CellContext`pt$$, #] + Subscript[$CellContext`range$$, $CellContext`scaled]}& , Range[$CellContext`plDims]]; $CellContext`doImage := Switch[$CellContext`p3D$$, Part[$CellContext`p3DList, 1], $CellContext`g2D, Part[$CellContext`p3DList, 2], $CellContext`g3D]; $CellContext`processOut[ Pattern[$CellContext`in$, Blank[]]] := ($CellContext`pPList = Map[$CellContext`pPos, $CellContext`fltrdSubPlot$$]; \ $CellContext`out = $CellContext`doImage; If[$CellContext`fileOut$$, $CellContext`mOutDo; \ $CellContext`doFileOut[ If[ And[$CellContext`fileOut$$, $CellContext`outFileType$$ != First[$CellContext`fileTypeList]], $CellContext`in$, 0]]]; If[ And[$CellContext`needsAnim8, Not[$CellContext`fileOnly$$]], AppendTo[$CellContext`loop, $CellContext`out]]; If[$CellContext`fileOnly$$, $CellContext`out = {}]); \ $CellContext`trkNotEqual := Or[$CellContext`showPtextTrk$$ != $CellContext`showPtext$$, \ $CellContext`pthRotTrk$$ != $CellContext`pthRot$$, $CellContext`showAxesTrk$$ != \ $CellContext`showAxes$$, $CellContext`stepsTrk$$ != $CellContext`steps$$, \ $CellContext`p3DTrk$$ != $CellContext`p3D$$, $CellContext`showEdgesTrk$$ != \ $CellContext`showEdges$$, $CellContext`physicsTrk$$ != \ $CellContext`physics$$, $CellContext`useDimLocsTrk$$ != \ $CellContext`useDimLocs$$, $CellContext`tTTrk$$ != $CellContext`tT$$]; \ $CellContext`setTrkEqual := {$CellContext`showPtextTrk$$ = \ $CellContext`showPtext$$; $CellContext`pthRotTrk$$ = $CellContext`pthRot$$; \ $CellContext`useDimLocsTrk$$ = $CellContext`useDimLocs$$; \ $CellContext`showAxesTrk$$ = $CellContext`showAxes$$; $CellContext`stepsTrk$$ = \ $CellContext`steps$$; $CellContext`p3DTrk$$ = $CellContext`p3D$$}; \ $CellContext`bANDNotEqual := Or[$CellContext`bAND1NameTrk$$ != $CellContext`bAND1Name$$, \ $CellContext`bAND2NameTrk$$ != $CellContext`bAND2Name$$]; \ $CellContext`edgeNotEqual := Or[$CellContext`showEdges$$ != $CellContext`showEdgesTrk$$, \ $CellContext`innerMagTrk$$ != $CellContext`innerMag$$, \ $CellContext`dimTrimTrk$$ != $CellContext`dimTrim$$, \ $CellContext`showClickVertsTrk$$ != $CellContext`showClickVerts$$, \ $CellContext`ltpsTrk$$ != $CellContext`ltps$$]; $CellContext`mainNotEqual := Or[$CellContext`trkNotEqual, $CellContext`refresh$$, \ $CellContext`selCoxeterTrk$$ != $CellContext`selCoxeter$$, \ $CellContext`bANDNotEqual, $CellContext`bANDTrk$$ != $CellContext`bAND$$, \ $CellContext`dsTrk$$ != $CellContext`ds$$, $CellContext`favoriteTrk$$ != \ $CellContext`favorite$$, $CellContext`newPTcd$$ != {}, \ $CellContext`locPtCdTrk$$ != $CellContext`locPtCdArr$$, $CellContext`lie$$ != "", $CellContext`fltrdSubPlotTrk$$ != \ $CellContext`fltrdSubPlot$$, $CellContext`edgeNotEqual, ToString[$CellContext`edgeValsTrk$$] != ToString[$CellContext`edgeVals$$], $CellContext`infileTrk$$ != \ $CellContext`infile$$]; If[$CellContext`mainNotEqual, If[$CellContext`dsTrk$$ != $CellContext`ds$$, \ $CellContext`dsTrk$$ = $CellContext`ds$$]; If[$CellContext`selCoxeterTrk$$ != $CellContext`selCoxeter$$, \ $CellContext`setPTcd[ Part[$CellContext`coxeterProjTbl, $CellContext`position[$CellContext`coxSubs, \ $CellContext`selCoxeter$$]]]; $CellContext`selCoxeterTrk$$ = \ $CellContext`selCoxeter$$, If[$CellContext`newPTcd$$ != {}, \ $CellContext`setPTcd[$CellContext`newPTcd$$]; $CellContext`newPTcd$$ = {}, If[$CellContext`favoriteTrk$$ != $CellContext`favorite$$, \ $CellContext`setPTcd[ Part[$CellContext`favorites, $CellContext`favorite$$]]; \ $CellContext`favoriteTrk$$ = $CellContext`favorite$$]]]; If[$CellContext`infileTrk$$ != $CellContext`infile$$, \ $CellContext`bAND1Name$$ = "inFile"; $CellContext`infileTrk$$ = $CellContext`infile$$]; If[ And[$CellContext`bAND$$ != 1, $CellContext`bAND1NameTrk$$ != $CellContext`bAND1Name$$], \ $CellContext`bANDTrk$$ = ($CellContext`bAND$$ = 1); $CellContext`switchFilter, If[ And[$CellContext`bAND$$ != 2, $CellContext`bAND2NameTrk$$ != \ $CellContext`bAND2Name$$], $CellContext`bANDTrk$$ = ($CellContext`bAND$$ = 2); $CellContext`switchFilter]]; If[$CellContext`bAND1NameTrk$$ != $CellContext`bAND1Name$$, \ $CellContext`bAND1NameTrk$$ = $CellContext`bAND1Name$$; \ $CellContext`bAND2NameTrk$$ = ($CellContext`bAND2Name$$ = ""); $CellContext`E8; If[$CellContext`bAND1Name$$ != "E8", $CellContext`dobAND1[$CellContext`bAND1Name$$]], If[$CellContext`bAND2NameTrk$$ != $CellContext`bAND2Name$$, \ $CellContext`bAND2NameTrk$$ = $CellContext`bAND2Name$$; \ $CellContext`bAND1NameTrk$$ = ($CellContext`bAND1Name$$ = ""); $CellContext`E8; \ $CellContext`dobAND2[$CellContext`bAND2Name$$]]]; If[$CellContext`trkNotEqual, $CellContext`setTrkEqual]; If[$CellContext`lie$$ != "", $CellContext`setLieGroup; $CellContext`lie$$ = ""]; If[$CellContext`bANDTrk$$ != $CellContext`bAND$$, \ $CellContext`switchFilter; $CellContext`bANDTrk$$ = $CellContext`bAND$$]; \ $CellContext`doFilter; If[ Or[$CellContext`fltrdSubPlotTrk$$ != \ $CellContext`fltrdSubPlot$$, $CellContext`tTTrk$$ != $CellContext`tT$$, And[$CellContext`needsEdges, Or[$CellContext`edgeNotEqual, ToString[$CellContext`edgeValsTrk$$] != ToString[$CellContext`edgeVals$$], \ $CellContext`physicsTrk$$ != $CellContext`physics$$]]], If[$CellContext`fltrdSubPlot$$ == {}, \ $CellContext`fullVerts$$ = {}, $CellContext`fullVerts$$ = Map[$CellContext`dsGet, $CellContext`fltrdSubPlot$$]]; If[ Or[$CellContext`tTTrk$$ != $CellContext`tT$$, And[$CellContext`tT$$ != {}, \ $CellContext`fltrdSubPlotTrk$$ != $CellContext`fltrdSubPlot$$]], \ $CellContext`tlines$$ = If[$CellContext`tT$$ == {}, {}, $CellContext`tLines]; \ $CellContext`tTTrk$$ = $CellContext`tT$$]; If[ And[$CellContext`needsEdges, Or[$CellContext`edgeNotEqual, \ $CellContext`fltrdSubPlotTrk$$ != $CellContext`fltrdSubPlot$$, And[ Not[$CellContext`edgeNotEqual], ToString[$CellContext`edgeValsTrk$$] != ToString[$CellContext`edgeVals$$]]]], \ $CellContext`getEdges]; If[ And[$CellContext`needsEdges, Or[$CellContext`edgeNotEqual, \ $CellContext`fltrdSubPlotTrk$$ != $CellContext`fltrdSubPlot$$, ToString[$CellContext`edgeValsTrk$$] != ToString[$CellContext`edgeVals$$]]], \ $CellContext`elines$$ = Flatten[ Map[$CellContext`eLines, $CellContext`edgeVals$$], 1]; $CellContext`edgeMag$$ = Max[$CellContext`chop, $CellContext`maxEdge]; \ $CellContext`elines$$ = ($CellContext`eSort$$ = $CellContext`elineSort[ If[$CellContext`eSteps$$ > 1, "Ascending", "Descending"]])]; If[ And[$CellContext`showClickVerts$$, Not[$CellContext`showClickVertsTrk$$]], If[$CellContext`physics$$, $CellContext`pLines, \ $CellContext`vLines][$CellContext`fltrdSubPlot$$], If[ Or[$CellContext`ltpsTrk$$ != $CellContext`ltps$$, \ $CellContext`fltrdSubPlotTrk$$ != $CellContext`fltrdSubPlot$$, \ $CellContext`physicsTrk$$ != $CellContext`physics$$], $CellContext`ltpsTrk$$ = \ $CellContext`ltps$$; $CellContext`clearClickVerts; If[$CellContext`physics$$, $CellContext`pLines, \ $CellContext`vLines][$CellContext`ltpsTrk$$]]]]; If[ Not[$CellContext`needsEdges], $CellContext`elines$$ = {}]; \ $CellContext`showEdgesTrk$$ = $CellContext`showEdges$$; \ $CellContext`dimTrimTrk$$ = $CellContext`dimTrim$$; \ $CellContext`showClickVertsTrk$$ = $CellContext`showClickVerts$$; \ $CellContext`innerMagTrk$$ = $CellContext`innerMag$$; \ $CellContext`edgeValsTrk$$ = $CellContext`edgeVals$$; \ $CellContext`physicsTrk$$ = $CellContext`physics$$; \ $CellContext`fltrdSubPlotTrk$$ = $CellContext`fltrdSubPlot$$; If[$CellContext`p3D$$ != Part[$CellContext`p3DList, 1], $CellContext`lastViewPoint$$ = { Part[ Subscript[$CellContext`xyVwPnt$$, $CellContext`scaled], 1], Part[ Subscript[$CellContext`xyVwPnt$$, $CellContext`scaled], 2], Subscript[$CellContext`zVwPnt$$, $CellContext`scaled]}]; If[$CellContext`useDimLocs$$, If[$CellContext`locPtCdTrk$$ != $CellContext`locPtCdArr$$, Switch[$CellContext`face$$, 1, $CellContext`H$$ = Part[$CellContext`locPtCdArr$$, All, 1]/$CellContext`zoomFct; $CellContext`V$$ = Part[$CellContext`locPtCdArr$$, All, 2]/$CellContext`zoomFct, 2, $CellContext`Z$$ = Part[$CellContext`locPtCdArr$$, All, 1]/$CellContext`zoomFct; $CellContext`H$$ = Part[$CellContext`locPtCdArr$$, All, 2]/$CellContext`zoomFct, 3, $CellContext`V$$ = Part[$CellContext`locPtCdArr$$, All, 1]/$CellContext`zoomFct; $CellContext`Z$$ = Part[$CellContext`locPtCdArr$$, All, 2]/$CellContext`zoomFct]]; $CellContext`initLocPtCds; \ $CellContext`showAxes$$ = True; $CellContext`steps$$ = ($CellContext`eSteps$$ = 1); $CellContext`anim8EdgeList$$ = False; $CellContext`p3D$$ = Part[$CellContext`p3DList, 1]]; $CellContext`showAxesTrk$$ = $CellContext`showAxes$$; \ $CellContext`stepsTrk$$ = $CellContext`steps$$; $CellContext`p3DTrk$$ = \ $CellContext`p3D$$; If[ Not[$CellContext`refresh$$], $CellContext`refresh$$ = True]; $CellContext`refresh$$ = False; $CellContext`out = $CellContext`outSav$$, If[$CellContext`needsAnim8, $CellContext`doAnim8, $CellContext`processOut[ 0]]; $CellContext`outSav$$ = $CellContext`out]]], \ $CellContext`localE8 = {$CellContext`p3DList, $CellContext`axesPt, \ $CellContext`Binary, $CellContext`BinSquare, $CellContext`BinStar, \ $CellContext`C6003D, $CellContext`callImage, $CellContext`Cell16, \ $CellContext`Cell24, $CellContext`Cell24D4, $CellContext`Cell24G2, \ $CellContext`clearClickVerts, $CellContext`clearFilter, \ $CellContext`clearPath, $CellContext`Cube2Pascal, $CellContext`Cube2Petrie, \ $CellContext`Cube3Pascal, $CellContext`Cube3Petrie, $CellContext`Cube4Pascal, \ $CellContext`Cube4Petrie, $CellContext`Cube5Pascal, $CellContext`Cube5Petrie, \ $CellContext`Cube6Pascal, $CellContext`Cube6Petrie, $CellContext`Cube7Pascal, \ $CellContext`Cube7Petrie, $CellContext`Cube8Pascal, $CellContext`Cube8Petrie, \ $CellContext`cylCnt, $CellContext`cylOK, $CellContext`Devolution, \ $CellContext`dimZeros, $CellContext`dln, $CellContext`dls, $CellContext`dlXn, \ $CellContext`dlYn, $CellContext`dlZn, $CellContext`dobAND1, \ $CellContext`dobAND2, $CellContext`doEdgeList, $CellContext`doFilter, \ $CellContext`doImage, $CellContext`doAnim8, $CellContext`dsGet, \ $CellContext`E4, $CellContext`E5, $CellContext`E6, $CellContext`E6a, \ $CellContext`E7, $CellContext`E8, $CellContext`E812x5, $CellContext`E824x10, \ $CellContext`E83, $CellContext`E83D, $CellContext`e8ExtrasInit, \ $CellContext`e8Filter, $CellContext`E8Hexes, $CellContext`E8Hyper, \ $CellContext`E8inE6, $CellContext`e8ListInit, $CellContext`E8Petrie, \ $CellContext`e8surf, $CellContext`e8Surface, $CellContext`edge1, \ $CellContext`edge2, $CellContext`edge3, $CellContext`edgeColor, \ $CellContext`edgeLines, $CellContext`eLines, $CellContext`elineSort, \ $CellContext`F4, $CellContext`F4G2, $CellContext`F4Star, $CellContext`F4Tris, \ $CellContext`faceGrids, $CellContext`faceList, $CellContext`filterList, \ $CellContext`final, $CellContext`findClicked, $CellContext`fPath, \ $CellContext`G2, $CellContext`g2D, $CellContext`g3D, $CellContext`getEdges, \ $CellContext`getU, $CellContext`getVContent, $CellContext`H4, \ $CellContext`HF, $CellContext`HI, $CellContext`Hydrogen, $CellContext`ifLen, \ $CellContext`ifNum, $CellContext`initial, $CellContext`initLocPtCds, \ $CellContext`iPath, $CellContext`labels, $CellContext`LeptonInfo, \ $CellContext`line2, $CellContext`line3, $CellContext`listToPos, \ $CellContext`loop, $CellContext`maxEdge, $CellContext`minEdgeCnt, \ $CellContext`nDRot, $CellContext`nDRots, $CellContext`needsArtPrint, \ $CellContext`needsAnim8, $CellContext`needsEdges, $CellContext`newLoc, \ $CellContext`nFaces, $CellContext`none, $CellContext`norm, \ $CellContext`nullPt, $CellContext`opacityOK, $CellContext`out, \ $CellContext`outerDim, $CellContext`outerDims, $CellContext`outerSum, \ $CellContext`param2D, $CellContext`param3D, $CellContext`params, \ $CellContext`particles, $CellContext`perim, $CellContext`physEdges, \ $CellContext`pLabels, $CellContext`plDims, $CellContext`pLines, \ $CellContext`pLocs, $CellContext`plotRange, $CellContext`pMassLife, \ $CellContext`polySurfaces, $CellContext`posDiff, $CellContext`posTbl, \ $CellContext`pPList, $CellContext`pPos, $CellContext`processImage, \ $CellContext`processOut, $CellContext`ptCds, $CellContext`pVecs, \ $CellContext`QuarkCol, $CellContext`QuarkInfo, $CellContext`rectifyEdges, \ $CellContext`rectifyParticles, $CellContext`rotXY, $CellContext`rotXYZ, \ $CellContext`rotYZ, $CellContext`rotZX, $CellContext`rot\[Theta]List, \ $CellContext`setFlt, $CellContext`setIFpath, $CellContext`setLieGroup, \ $CellContext`setPTcd, $CellContext`setPthPrm, $CellContext`setPTo, \ $CellContext`setPTt, $CellContext`sphericalRegion, $CellContext`surfaces, \ $CellContext`switchFilter, $CellContext`Tesseract, $CellContext`tickRange, \ $CellContext`tickRangeCalc, $CellContext`tLines, $CellContext`tly1, \ $CellContext`transOuter, $CellContext`triLines, $CellContext`unsetFlt, \ $CellContext`vertEdges, $CellContext`vertexTally, $CellContext`VF, \ $CellContext`VI, $CellContext`viewAngle, $CellContext`viewCenter, \ $CellContext`viewPoint, $CellContext`vLines, $CellContext`vLineTally, \ $CellContext`zeroPt, $CellContext`ZF, $CellContext`ZI, $CellContext`\[Theta], \ $CellContext`trkNotEqual, $CellContext`setTrkEqual}, $CellContext`chop = 0.0001, $CellContext`dims := Length[ Part[$CellContext`dl, $CellContext`ds$$]], $CellContext`dl = {{ "1", "2", "3", "4", "5", "6", "7", "8"}, { "\!\(\*SubscriptBox[\(\[Omega]\), \(S\)]\)", "\!\(\*SubscriptBox[\(\[ImaginaryI]\[Omega]\), \(T\)]\)", "U", "V", "\[ImaginaryI]\[Omega]", "r", "g", "b"}, { "\!\(\*SubscriptBox[\(\[Omega]\), \(S\)]\)", "\!\(\*SubscriptBox[\(\[ImaginaryI]\[Omega]\), \(T\)]\)", "W", "Y", "\[ImaginaryI]\[Omega]", "x", "\!\(\*SuperscriptBox[\(g\), \(3\)]\)", "\!\(\*SuperscriptBox[\(g\), \(8\)]\)"}, { "1", "2", "3", "4", "5", "6", "7", "8"}, { "1", "2", "3", "4", "5", "6", "7", "8"}}, $CellContext`pBin[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8bin, Min[$CellContext`p, 256]], $CellContext`e8bin = CompressedData[" 1:eJylkt2RwjAMhL08XRvXEiXQAP2/cQzez7FknQOYyRDL0v45v7f79XZpf0ut /bSx9OWL5Ip8Inf4oUjX8+XNwdMD28ayIR087YkjZiFBFXakUemE6gQ6VF8w hqCF137mDdMGN8pEe1LoVmApLAnqNjbEJWEisu0CMAERRxgYsXCBki2Y2pDj WMaQsdSmMT+dYcB4eIZDNCkQv3Ss8HOzd4Ge1LgmaaKIsri2pbxNMGUgKQjb KQwno9gMhqLdQmASRgxBQIojAOZY+GAkNBp7lGUQtblNbdmOamLVYbOAIeY1 HG6JXZoYIg3XUNBxHf/TFsGkQJATjCdZwUgpLxDXMrlAaZCMrdq6jI3iGDub NmydbA9C92MY/PCP9QCHvgWy "], $CellContext`pC600[ Pattern[$CellContext`p, Blank[]]] := Dot[$CellContext`C600, $CellContext`pE8[$CellContext`p]], $CellContext`C600 = {{ 1/2, (1 + Sqrt[5])/4, 0, (-1)/2, (1 + Sqrt[5])/4, 0, 0, 0}, {(1 + Sqrt[5])/4, 0, 1/2, (1 + Sqrt[5])/4, 0, (-1)/2, 0, 0}, {(-1)/2, 1/2, (1 + Sqrt[5])/4, (1 + Sqrt[5])/4, 0, 0, 0, 0}, { 0, 1/2, (1 + Sqrt[5])/4, 0, (-1)/2, (1 + Sqrt[5])/4, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}}, $CellContext`favorites = {{{1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}}, {{-0.18479253090409503`, 0.18479253090409517`, -0.06417777247591215, 1, -0.3472963553338604, 0.3472963553338602, 0, 0}, { 0.6840402866513372, 0.6840402866513374, 0, 0, 0.23756469845553865`, 0.23756469845553885`, 0.3639702342662021, 0.3639702342662021}, {-0.18479253090409503`, 0.18479253090409517`, -0.06417777247591215, 1, -0.3472963553338604, 0.3472963553338602, 0, 0}}, {{ 1/2, 1/(2 Sqrt[2]), 0, (-1)/(2 Sqrt[2]), 1/2, (-1)/(2 Sqrt[2]), 0, 1/(2 Sqrt[2])}, { 0, 1/(2 Sqrt[2]), 1/2, 1/(2 Sqrt[2]), 0, (-1)/(2 Sqrt[2]), (-1)/ 2, (-1)/(2 Sqrt[2])}, {-(1/Sqrt[2]), 1/2, 0, (-1)/ 2, -(1/Sqrt[2]), (-1)/2, 0, 1/2}}, {{0.594095480117793, 0.392376873691752, 0.193033322933216, 0.107623126308248, 0.0940954801177932, -0.455898878992783, -0.416640120683195, \ -0.232292081242804}, {-0.0940954801177932, 0.455898878992783, 0.416640120683195, 0.232292081242804, 0.594095480117793, 0.392376873691752, 0.193033322933216, 0.107623126308248}, {-(1/Sqrt[2]), 1/2, 0, (-1)/ 2, -(1/Sqrt[2]), (-1)/2, 0, 1/2}}, {{ 73/(2 Sqrt[6458]), 67/(2 Sqrt[6458]), 53/(2 Sqrt[6458]), 17/(2 Sqrt[6458]), (-17)/(2 Sqrt[6458]), (-53)/(2 Sqrt[6458]), (-67)/( 2 Sqrt[6458]), (-73)/(2 Sqrt[6458])}, { 17/(2 Sqrt[6458]), 53/(2 Sqrt[6458]), 67/(2 Sqrt[6458]), 73/(2 Sqrt[6458]), 73/(2 Sqrt[6458]), 67/(2 Sqrt[6458]), 53/(2 Sqrt[6458]), 17/(2 Sqrt[6458])}, {0, 0, 0, 0, 0, 1, 0, 0}}, {{ 7/Sqrt[155], 4/Sqrt[155], 7/(2 Sqrt[155]), (-1)/(2 Sqrt[155]), -(1/Sqrt[155]), (-2)/Sqrt[155], (-11)/(2 Sqrt[155]), (-13)/(2 Sqrt[155])}, { 1/Sqrt[155], 2/Sqrt[155], 11/(2 Sqrt[155]), 13/(2 Sqrt[155]), 7/ Sqrt[155], 4/Sqrt[155], 7/(2 Sqrt[155]), (-1)/(2 Sqrt[155])}, {0, 0, 0, 0, 0, 1, 0, 0}}, {{ 0, 0, 0.9191539418989376, 0, 0, 0.09901705165447641, 0, 0}, { 0.4595769709494688, 0.09901705165447641, 0, 0.9191539418989376, 0, 0, 0, 0}, { 0, 0.4595769709494688, 0.09901705165447641, 0.9191539418989376, 0, 0, 0, 0}}, {{0, 0, 1, 0, 0, 0, 0, 0}, { Sqrt[2/7], 0, 0, Sqrt[5/7], 0, 0, 0, 0}, {0, Sqrt[2/7], 0, Sqrt[5/7], 0, 0, 0, 0}}, {{ 1/2, 1/(2 Sqrt[2]), 0, (-1)/(2 Sqrt[2]), 0, 0, 0, 0}, { 0, 1/(2 Sqrt[2]), 1/2, 1/(2 Sqrt[2]), 0, 0, 0, 0}, { 1/Sqrt[2], (-1)/2, 0, 1/2, 0, 0, 0, 0}}, {{ 1/2, (1 + Sqrt[5])/8, (-1 + Sqrt[5])/8, (1 - Sqrt[5])/ 8, (-1 - Sqrt[5])/8, 0, 0, 0}, { 0, Sqrt[5/8 - Sqrt[5]/8]/2, Sqrt[5/8 + Sqrt[5]/8]/2, Sqrt[5/8 + Sqrt[5]/8]/2, Sqrt[5/8 - Sqrt[5]/8]/2, 0, 0, 0}, {(Sqrt[5/8 - Sqrt[5]/8] + (1 + Sqrt[5])/4)/ 2, ((1 - Sqrt[5])/4 - Sqrt[5/8 + Sqrt[5]/8])/ 2, ((1 - Sqrt[5])/4 + Sqrt[5/8 + Sqrt[5]/8])/ 2, (-Sqrt[5/8 - Sqrt[5]/8] + (1 + Sqrt[5])/4)/2, (-1)/2, 0, 0, 0}}, {{1/2, Cos[Pi/7]/2, Sin[(3 Pi)/14]/2, Sin[Pi/14]/2, - Sin[Pi/14]/2, -Sin[(3 Pi)/14]/2, -Cos[Pi/7]/2, 0}, { 0, Sin[Pi/7]/2, Cos[(3 Pi)/14]/2, Cos[Pi/14]/2, Cos[Pi/14]/2, Cos[(3 Pi)/14]/2, Sin[Pi/7]/2, 0}, {(Cos[Pi/7] + Sin[Pi/7])/ 2, (-Cos[(3 Pi)/14] - Sin[(3 Pi)/14])/ 2, (Cos[Pi/14] + Sin[Pi/14])/2, (-Cos[Pi/14] + Sin[Pi/14])/ 2, (Cos[(3 Pi)/14] - Sin[(3 Pi)/14])/2, (Cos[Pi/7] - Sin[Pi/7])/ 2, (-1)/2, 0}}, {{-0.3938985035407526, 0., 0., 0.9191539418989375, 0., 0., 0., 0.}, {0., 0.3938985035407526, -0.9191539418989375, 0., 0., 0., 0., 0.}, { 1.0203150588323422`, 0., 0., 0.27852830295289943`, 0., 0., 0., 0.}}, {{0, -0.5567934404522487, -0.38529087617102353`, 0.38529087617102353`, 0.08054772639440973, -0.1969492517703763, 0, 0.1969492517703763}, { 0.7663604248754179, 0, 0.09901705165447641, 0.09901705165447641, 0, 0.16021295504274685`, 0.18091315553621942`, 0.16021295504274685`}, { 0, 0.7663604248754179, 0.09901705165447641, 0.09901705165447641, 0, 0.16021295504274685`, 0.18091315553621942`, 0.16021295504274685`}}, {{ 0, -0.5567934404522487, 0.38529087617102353`, -0.38529087617102353`, 0.08054772639440973, -0.1969492517703763, 0, 0.1969492517703763}, { 0.18091315553621942`, 0, 0.09901705165447641, 0.09901705165447641, 0, 0.16021295504274685`, 0.7663604248754179, 0.16021295504274685`}, { 0, 0.18091315553621942`, 0.09901705165447641, 0.09901705165447641, 0, 0.16021295504274685`, 0.7663604248754179, 0.16021295504274685`}}, {{ 0, -0.5567934404522487, 0.1969492517703763, -0.1969492517703763, 0.08054772639440973, -0.38529087617102353`, 0, 0.38529087617102353`}, { 0.18091315553621942`, 0, 0.16021295504274685`, 0.16021295504274685`, 0, 0.09901705165447641, 0.7663604248754179, 0.09901705165447641}, { 0, -0.08054772639440973, -0.1969492517703763, 0.1969492517703763, 0.5567934404522487, 0.38529087617102353`, 0, -0.38529087617102353`}}, {{ 0, -0.5567934404522487, 0.1969492517703763, -0.1969492517703763, 0.08054772639440973, -0.38529087617102353`, 0, 0.38529087617102353`}, { 0.18091315553621942`, 0, 0.16021295504274685`, 0.16021295504274685`, 0, 0.09901705165447641, 0.7663604248754179, 0.09901705165447641}, { 0.3204259100854937, 0, 0, -0.3204259100854937, 0.6408518201709874, 0.3204259100854937, 0, -0.3204259100854937}}, {{(-1)/2, (-1)/2, 0, 0.5448835825396743, 0.08054772639440973, 0, 0.38529087617102353`, 0.2785283029528995}, { 0.5448835825396743, -0.5448835825396743, 0.38529087617102353`, 0, 0, -0.2785283029528995, 0, 0}, {-0.5448835825396743, 0.5448835825396743, 0, 0.38529087617102353`, 0, -0.2785283029528995, 0, 0}}, {{ 0, 0, 0, 1/Sqrt[2], 0, 0, 0, 1/Sqrt[2]}, { 0, 1/Sqrt[3], -(1/Sqrt[6]), 0, 0, 0, 1/Sqrt[2], 0}, { 1/(2 Sqrt[3]), 1/(2 Sqrt[3]), -(1/Sqrt[6]), 1/Sqrt[6], 0, -(1/Sqrt[2]), 0, 0}}, {{0., 0., 0., 0.5448835825396742, 0., -0.38529087617102364`, 0., 0.5448835825396743}, {0., 0.5773502691896258, -0.27852830295289943`, 0., 0.38529087617102353`, 0., 0.5448835825396742, 0.}, {-0.18834162440064725`, 0.5822401279413998, -0.27852830295289943`, 0., 0., 0., 0., 0.}}, {{-0.3938985035407526, 0., 0., 0.9191539418989375, 0., 0., 0., 0.}, {0., 0.3938985035407526, -0.9191539418989375, 0., 0., 0., 0., 0.}, {1.0203150588323422`, 0., 0., 0.27852830295289943`, 0., 0., 0., 0.}}, {{2 - 4/Sqrt[3], 0, 0, -Sqrt[2/3] + Sqrt[2], 0, 0, Sqrt[2], 0}, { 0, -2 + 4/Sqrt[3], Sqrt[2/3] - Sqrt[2], 0, 0, 0, 0, -Sqrt[2]}, { 0, 2 - 4/Sqrt[3], 0, Sqrt[2] (-1 + 1/Sqrt[3]), 0, 0, -(1/Sqrt[2]), -Sqrt[3/2]}}, {{(1 - Sqrt[3])/2, 0, 1/2, 1/2, 0, 0, 0, 0}, {0, (-1 + Sqrt[3])/2, (-1)/2, 1/2, 0, 0, 0, 0}, { 1, 0, ((-1)/2 + Sqrt[3])/2, ((-1)/2 + Sqrt[3])/2, 0, 0, 0, 0}}, {{ 0., -0.08054772639440973, 0.5448835825396742, 0., 0.5567934404522487, 0., 0.27852830295289943`, 0.}, { 0.7663604248754179, 0., 0., 0.14003125735595784`, 0., 0.28944824449197154`, 0., 0.016901642927438763`}, {0., 0.5567934404522487, 0.5448835825396742, 0., -0.08054772639440973, 0., 0.27852830295289943`, 0.}}, {{1/2, (-1)/4, 1/(2 Sqrt[2]), 1/(4 Sqrt[2]), 0, 0, (-1)/(2 Sqrt[2]), (-1)/(4 Sqrt[2])}, { 0, 0, 1/(2 Sqrt[2]), 1/(4 Sqrt[2]), 1/2, 1/4, 1/(2 Sqrt[2]), 1/(4 Sqrt[2])}, {-(1/Sqrt[2]), (-1)/(2 Sqrt[2]), 1/2, 1/4, 0, 0, (-1)/ 2, (-1)/4}}, {{-0.5418986532624117, -0.5418986532624117, 0, 0.5448835825396743, 0.08054772639440973, 0, 0.38529087617102353`, 0.2785283029528995}, { 0.5448835825396743, -0.5448835825396743, 0.38529087617102353`, 0, 0, -0.2785283029528995, 0, 0}, { 0, 0.5448835825396743, -0.5448835825396743, 0.38529087617102353`, -0.2785283029528995, 0, 0, 0}}, {{0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, { 0, 0, (-1)/2, (-1)/2, 0, Sqrt[2]/9 + ((-1)/(2 Sqrt[2]) - 1/(3 Sqrt[6]))/Sqrt[ 3] + (1/(2 Sqrt[2]) - 1/(3 Sqrt[6]))/Sqrt[ 3], -(((-1)/(2 Sqrt[2]) - 1/(3 Sqrt[6]))/Sqrt[2]) + ( 1/(2 Sqrt[2]) - 1/(3 Sqrt[6]))/Sqrt[2], 2/9 - ((-1)/(2 Sqrt[2]) - 1/(3 Sqrt[6]))/Sqrt[ 6] - (1/(2 Sqrt[2]) - 1/(3 Sqrt[6]))/Sqrt[6]}}, {{ 1/2, 1/2, 1/2, 1/2, 0, 0, 0, 0}, {(-3)/(2 Sqrt[5]), (-1)/(2 Sqrt[5]), 1/(2 Sqrt[5]), 3/(2 Sqrt[5]), 0, 0, 0, 0}, { 3/(2 Sqrt[5]), 1/(2 Sqrt[5]), (-1)/(2 Sqrt[5]), (-3)/(2 Sqrt[5]), 0, 0, 0, 0}}, {{ 1/Sqrt[5], 1/Sqrt[5], 1/Sqrt[5], 1/Sqrt[5], 1/Sqrt[5], 0, 0, 0}, {-Sqrt[2/5], -(1/Sqrt[10]), 0, 1/Sqrt[10], Sqrt[2/5], 0, 0, 0}, {-Sqrt[2/5], -(1/Sqrt[10]), 0, 1/Sqrt[10], Sqrt[2/5], 0, 0, 0}}, {{ 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 0}, {(-3)/(2 Sqrt[7]), -(1/Sqrt[7]), (-1)/(2 Sqrt[7]), 0, 1/(2 Sqrt[7]), 1/Sqrt[7], 3/(2 Sqrt[7]), 0}, {(-3)/(2 Sqrt[7]), -(1/Sqrt[7]), (-1)/(2 Sqrt[7]), 0, 1/(2 Sqrt[7]), 1/ Sqrt[7], 3/(2 Sqrt[7]), 0}}, {{ 1/Sqrt[3], 0, 0, 0, 1/Sqrt[3], 0, 0, 1/Sqrt[3]}, { 0, 1/Sqrt[3], 0, 1/Sqrt[3], 0, 0, 1/Sqrt[3], 0}, { 1/Sqrt[3], 0, 1/Sqrt[3], 0, 0, 1/Sqrt[3], 0, 0}}, {{0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, -1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}}, {{ 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}}, {{ 2/Sqrt[233], (-13)/(4 Sqrt[233]), 0, 0, 0, 0, 0, 0}, { 0, 0, 1/4, 0, 0, 0, 0, 0}, {1/4, 0, (-1)/4, 0, 0, 0, 0, 0}}, {{ 0.15933529171166458`, 0., 0.19264543808551174`, 0., -0.15933529171166458`, 0., -0.19264543808551174`, 0.}, {0., 0.23681839510290936`, 0., 0.08010647752137343, 0., -0.23681839510290936`, 0., -0.08010647752137343}, { 0, -0.08010647752137343, 0, 0.23681839510290936`, 0, 0.08010647752137343, 0, -0.23681839510290936`}}, {{ 1/2, 0, 0, 0, (-1)/2, 0, 0, 0}, {0, 1/2, 0, 0, 0, (-1)/2, 0, 0}, { 0, 0, 1/2, 0, 0, 0, (-1)/2, 0}}, {{0.5, 0.8090169943749475, 0., -0.5, 0.8090169943749475, 0., 0., 0.}, {0.8090169943749475, 0., 0.5, 0.8090169943749475, 0., -0.5, 0., 0.}, {0., 0.5, 0.8090169943749475, 0., -0.5, 0.8090169943749475, 0., 0.}}}, $CellContext`auxData$$ = False, $CellContext`le8 = 256, $CellContext`pls = {CompressedData[" 1:eJwd0wOfEAYAxuEue7Va1lXbsm1zC5ddl3XZ5rK11dJybbll27Zt20+9v//z Ed7A4DZBIQGhLOB7oUIThrCEIzwRiEgkIhOFqEQjOj8Qg5j8SCxi8xNxiEs8 4pOAhCQiMUlISjICSU4KUvIzv/ArqUhNGtKSjvRkICOZyEwWspKN7OQgJ7nI TR7yko/8FKAghShMEYpSjOKUoCSlKE0ZyvIbv1OO8lSgIkFUojJVqEo1qlOD mtSiNnWoSz3q04BgGtKIxjShKc1oTgta0orWhNCGtrSjPR3oSCc604WudKM7 PehJL3rTh770oz8DGMggBvMHQxjKMIYzgpGMYjRjGMs4xjOBiUxiMlP4k7+Y yjT+ZjozmMksZvMPc5jLPOazgIUsYjFL+Jf/WMoylrOClaxiNWv4n7WsYz0b 2MgmNrOFrWxjOzvYyS52s4e97GM/BzjIIQ5zhKMc4zgnOMkpTnOGs5zjPBe4 yCUuc4WrXOM6N7jJLW5zh7vc4z4PeMgjHvOEpzzjOS94ySte84a3vOM9H/jI 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251, 255}, CompressedData[" 1:eJwl0stPDwAAwPGfyWRcROVtljIJGVPyygEzHIqDUqMfigtDD++8H8njWF5h 5XEgB8xwyCtiTB6xyMEzES6MlubTHD77/gPfQcEVqcs7BAKBKtrbkRA60ZlQ utCVbnQnjB70JJwIIulFb/rQl370ZwADiWIw0cQwhKHEMow4hjOCkcQzitGM YSwJJDKOJMYzgYlMYjLJTGEq05jODGYyi9mkkMoc5jKPNNKZTwaZLGAhWQRZ xGKWkE0OS1nGSlaxmlzyyKeANaxlHevZwEY2UchmtrCVbWxnBzvZxW72UMRe itnHfg5wkBJKOcRhjnCUY5RxnBOcpJwKTnGaM5zlHOep5AIXucRlrnCVa1wP /H/mBje5xW3uUM1d7lHDfR7wkEc8ppYnPOUZz6njBS+p5xWvaeANb3nHez7w kU808pkmvvCVZr7xnR/85Be/+UMLrfyljfb5/wHxuGHV "], {2, 3, 4, 5, 6, 7, 8, 9, 38, 39, 40, 49, 50, 51, 52, 53, 62, 63, 64, 73, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 184, 193, 194, 195, 204, 205, 206, 207, 208, 217, 218, 219, 248, 249, 250, 251, 252, 253, 254, 255}, CompressedData[" 1:eJwl0kdbDwAAwOG/a5ERla3UgYRTVg6yesjIB0ApCpVZQohssrJCGV9AMp5k HUI4oehARkZkl1y9PR3e5/cFfpFpuQtyugUCgXt0NohgutODEHrSi970IZS+ 9COMcCLozwAGMojBDGEow4gkiuFEE8MIRhLLKOIYzRjGEs84xjOBiUwigclM 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121, 122, 123, 126, 128, 129, 131, 134, 135, 136, 137, 138, 140, 141, 146, 147, 148, 150, 152, 158, 159, 160, 161, 162, 163, 168, 170, 173, 177, 179, 183, 184, 185, 186, 188, 195, 197, 200, 203, 205, 206, 207, 208, 209, 210, 211, 212, 213, 215, 216, 217, 218, 219, 221, 222, 227, 228, 229, 231, 232, 234, 240, 243, 245, 246}, $CellContext`triList = { "T1", "T1p", "T2", "T2p", "T4", "T4p"}, $CellContext`dsNames = { "binary", "e8", "physics", "CELL600"}, $CellContext`doProj[ Pattern[$CellContext`n$, Blank[]]] := {$CellContext`H$$ = Flatten[ Join[ Table[{$CellContext`a = Cos[($CellContext`i - 1) 2 (Pi/$CellContext`n$)], $CellContext`a/ 2}, {$CellContext`i, $CellContext`j = Ceiling[$CellContext`n$/2]}], Array[0& , $CellContext`dims - 2 $CellContext`j]]]/2; Part[$CellContext`H$$, 2] = - Part[$CellContext`H$$, 2]; $CellContext`H$$, $CellContext`V$$ = Flatten[ Join[ Table[{$CellContext`a = Sin[($CellContext`i - 1) 2 (Pi/$CellContext`n$)], $CellContext`a/ 2}, {$CellContext`i, $CellContext`j = Ceiling[$CellContext`n$/2]}], Array[0& , $CellContext`dims - 2 $CellContext`j]]]/ 2, $CellContext`Z$$ = Flatten[ Join[-Table[{$CellContext`a = (-1)^($CellContext`i + 1) Cos[($CellContext`n$ - $CellContext`i) 2 (Pi/$CellContext`n$)] + (-1)^$CellContext`i Sin[($CellContext`n$ - $CellContext`i) 2 (Pi/$CellContext`n$)], $CellContext`a/ 2}, {$CellContext`i, $CellContext`j = Ceiling[$CellContext`n$/2]}], Array[0& , $CellContext`dims - 2 $CellContext`j]]]/ 2}, $CellContext`fileTypeList = { ".avi", ".bmp", ".dxf", ".eps", ".gif", ".jpeg", ".html", ".obj", ".lwo", ".Maya", ".MathML", ".pdf", ".png", ".stl", ".svg", ".tiff", ".vrml", ".wmf", ".x3d", ".xls", ".lsl", ".tri"}, $CellContext`hydrogen = {192, 198, 44, 66}, $CellContext`plNames = { "All", "E8=!Excluded", "8Ortho=Exc", "D8=Odd=Int", "E7", "D7=SO(14)", "C8=7Cube=Int/2", "E6", "D6=SO(12)", "6Cube=Hexeract", "E5", "D5=SO(10)", "A4=SL(5)=E4", "C4=5Cube", "D4=SO(8)", "F4", "F4s=24CellDual", "24Cell", "16Cell", "8Cell=4Cube", "H4", "H4/\[Phi]", "A3=D3=SO(6)", "3Cube", "D2=SO(4)", "B2=SO(5)=C2", "G2s=gluons", "HammingCode", "!Anti", "Anti", "!pType", "pType", "!Color", "Color", "!Spin", "Spin", "!Generation", "Generation", "First30", "None"}, $CellContext`doCubePascal[ Pattern[$CellContext`n$, Blank[]]] := {$CellContext`H$$ = Normalize[ Join[ Array[1& , $CellContext`n$], Array[0& , 8 - $CellContext`n$]]], $CellContext`V$$ = Normalize[ Join[ Table[$CellContext`i, {$CellContext`i, -($CellContext`n$ - 1), $CellContext`n$ - 1, 2}], Array[0& , 8 - $CellContext`n$]]], $CellContext`Z$$ = Normalize[ Join[ Table[(-1)^$CellContext`i ($CellContext`i/ 2), {$CellContext`i, -($CellContext`n$ - 1), $CellContext`n$ - 1, 2}], Array[0& , 8 - $CellContext`n$]]]}, $CellContext`doCube[ Pattern[$CellContext`n$, Blank[]]] := {$CellContext`H$$ = Join[ Table[ Cos[($CellContext`i - 1) ( Pi/$CellContext`n$)], {$CellContext`i, Min[$CellContext`dims, $CellContext`n$]}], Array[0& , Max[0, $CellContext`dims - $CellContext`n$]]]/ 2, $CellContext`V$$ = Join[ Table[ Sin[($CellContext`i - 1) ( Pi/$CellContext`n$)], {$CellContext`i, Min[$CellContext`dims, $CellContext`n$]}], Array[0& , Max[0, $CellContext`dims - $CellContext`n$]]]/ 2, $CellContext`Z$$ = Join[-Table[(-1)^($CellContext`i + 1) Cos[($CellContext`n$ - $CellContext`i) ( Pi/$CellContext`n$)] + (-1)^$CellContext`i Sin[($CellContext`n$ - $CellContext`i) ( Pi/$CellContext`n$)], {$CellContext`i, Min[$CellContext`dims, $CellContext`n$]}], Array[0& , Max[0, $CellContext`dims - $CellContext`n$]]]/ 2}, $CellContext`H1a = {1, 2, 3, 4}, $CellContext`V1a = {6, 7, 8}, $CellContext`Z1a = {5}, $CellContext`q = {66, 75, 210, 55, 67, 76, 211, 56, 68, 77, 212, 57, 243, 237, 232, 228, 242, 236, 231, 227, 241, 235, 230, 226, 225, 154, 144, 124, 224, 153, 143, 123, 223, 152, 142, 122, 177, 186, 197, 42, 178, 187, 198, 43, 179, 188, 199, 44, 147, 127, 161, 157, 146, 126, 160, 156, 145, 125, 159, 155, 108, 37, 138, 118, 107, 36, 137, 117, 106, 35, 136, 116}, $CellContext`a1 = {51, 206}, $CellContext`a2 = {50, 51, 63, 194, 206, 207}, $CellContext`a3 = {49, 50, 51, 62, 63, 73, 184, 194, 195, 206, 207, 208}, $CellContext`a4 = {48, 49, 50, 51, 61, 62, 63, 72, 73, 81, 176, 184, 185, 194, 195, 196, 206, 207, 208, 209}, $CellContext`a5 = {47, 48, 49, 50, 51, 60, 61, 62, 63, 71, 72, 73, 80, 81, 87, 170, 176, 177, 184, 185, 186, 194, 195, 196, 197, 206, 207, 208, 209, 210}, $CellContext`a6 = {46, 47, 48, 49, 50, 51, 59, 60, 61, 62, 63, 70, 71, 72, 73, 79, 80, 81, 86, 87, 91, 166, 170, 171, 176, 177, 178, 184, 185, 186, 187, 194, 195, 196, 197, 198, 206, 207, 208, 209, 210, 211}, $CellContext`a7 = {45, 46, 47, 48, 49, 50, 51, 58, 59, 60, 61, 62, 63, 69, 70, 71, 72, 73, 78, 79, 80, 81, 85, 86, 87, 90, 91, 93, 164, 166, 167, 170, 171, 172, 176, 177, 178, 179, 184, 185, 186, 187, 188, 194, 195, 196, 197, 198, 199, 206, 207, 208, 209, 210, 211, 212}, $CellContext`b2 = {1, 97, 102, 155, 160, 256}, $CellContext`b3 = {1, 97, 99, 101, 102, 109, 148, 155, 156, 158, 160, 256}, $CellContext`b4 = {1, 97, 99, 100, 101, 102, 107, 108, 109, 116, 141, 148, 149, 150, 155, 156, 157, 158, 160, 256}, $CellContext`b5 = {1, 97, 98, 99, 100, 101, 102, 106, 107, 108, 109, 112, 115, 116, 120, 137, 141, 142, 145, 148, 149, 150, 151, 155, 156, 157, 158, 159, 160, 256}, $CellContext`b6 = {1, 96, 97, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 119, 120, 124, 133, 137, 138, 141, 142, 143, 144, 145, 148, 149, 150, 151, 152, 155, 156, 157, 158, 159, 160, 161, 256}, $CellContext`b8 = CompressedData[" 1:eJwt0cVWFAAAheFhK91I5wvxACBDSc0ISDeS0kiHAr4WrdKdWz7OcfGdf33P zQuGi0MRgUCgn/d+IJIoookhljjiSSCRJJJJIZU0PpJOBplkkU0OueSRTwGF FFFCKZ8oI0g5FVRSRTWfqaGWOuppIESYLzTSRDNfaaGVNtrpoJMuuumhl77/ +wcY5BtDDDPCKGOM850JJplimhlmmWOeHyywyBLLrLDKGutssMlPfrHFNjv8 Zpc99jngkCOO+cNf/nHCKWecc8ElV1xzwy133PPAI08888Ir7+e/AbEEQXU= "], $CellContext`c3 = {1, 97, 99, 101, 102, 109, 148, 155, 156, 158, 160, 256}, $CellContext`c4 = {1, 97, 99, 100, 101, 102, 107, 108, 109, 116, 141, 148, 149, 150, 155, 156, 157, 158, 160, 256}, $CellContext`c5 = {1, 97, 98, 99, 100, 101, 102, 106, 107, 108, 109, 112, 115, 116, 120, 137, 141, 142, 145, 148, 149, 150, 151, 155, 156, 157, 158, 159, 160, 256}, $CellContext`c6 = {1, 96, 97, 98, 99, 100, 101, 102, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 119, 120, 124, 133, 137, 138, 141, 142, 143, 144, 145, 148, 149, 150, 151, 152, 155, 156, 157, 158, 159, 160, 161, 256}, $CellContext`c7 = {1, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 118, 119, 120, 122, 123, 124, 126, 131, 133, 134, 135, 137, 138, 139, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 155, 156, 157, 158, 159, 160, 161, 162, 256}, $CellContext`c8 = CompressedData[" 1:eJwt0cVWFAAAheFhK91I5wvxACBDSc0ISDeS0kiHAr4WrdKdWz7OcfGdf33P zQuGi0MRgUCgn/d+IJIoookhljjiSSCRJJJJIZU0PpJOBplkkU0OueSRTwGF FFFCKZ8oI0g5FVRSRTWfqaGWOuppIESYLzTSRDNfaaGVNtrpoJMuuumhl77/ 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186, 187, 190, 191, 192, 193, 194, 195, 196, 197, 198, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 214, 215, 216, 217, 218, 219}, $CellContext`d8 = {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219}, $CellContext`e6 = {1, 10, 11, 12, 13, 17, 18, 19, 23, 24, 28, 38, 39, 40, 41, 48, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 65, 72, 73, 74, 81, 94, 95, 99, 109, 128, 129, 148, 158, 162, 163, 176, 183, 184, 185, 192, 193, 194, 195, 196, 203, 204, 205, 206, 207, 208, 209, 216, 217, 218, 219, 229, 233, 234, 238, 239, 240, 244, 245, 246, 247, 256}, $CellContext`e7 = CompressedData[" 1:eJwV0bkvHQAAwOFnVSSORCWaMDgX6lxctbgW3mIRpCQWfWKpRSiJhUWCRdIm iMWCxbW4FzdL0S4SkpI4Etfa7w1ffn/AL/VrVzAUEQgE+gg3kg9EEU0MscQR TwKJfCSJZD6RQhrpZJBJFtnkkMtn8singEKKKKaEUsoop4IvVFJFNTXUUkc9 DQRppIlmWmiljXY66OQbIbr5Tg+99PODAQYZYpgRRhljnAkm+ckvpphmhlnm mGeBRZZYZoVV1lhng0222GaHXfbY54BDjjjmhFPO+M05F1zyh79ccc0N/7jl jnseeOSJZ1545Y13wtP/AxcSQHI= "], $CellContext`e8 = CompressedData[" 1:eJwl01N3FgAAgOGv27Tccsu2bddq2bWsLdu2W7Zt27Zt27c9O1085/0Fb0h4 ZFhEjEAg8I3oxiQWsYlDXIKIR3wSkJBEJCYJSQkmGclJQUpSkZo0pCWEdKQn AxnJRGaykJVsZCcHOclFbvKQl3zkpwAFKURhilCUYhSnBCUpRWnKUJZylKcC FalEZapQlWpUpwY1qUUotalDGHWpR30a0JBGNKYJTWlGc1rQkla0Jpw2tKUd 7elARzrRmS50pRsRRNKdHvSkF73pQ1/60Z8BDGQQgxnCUIYxnBGMZBSjGcNY xjGeCUxkEpOZwlSmMZ0ZzGQWs5lDFHOZx3wWsJBFLGYJS1nGclawklWsZg1r Wcd6NrCRTWxmC1vZxnZ2sJNd7GYPe9nHfg5wkEMc5ghHOcZxTnCSU5zmDGc5 x3kucJFLXOYKV7nGdW5wk1vc5g53ucd9HvCQRzzmCU95xnNe8JJXvOYNb3nH ez7wkU985gtfA////M4PfvKL3/zhL9Hz/gNnDnod "], $CellContext`g2 = {50, 51, 63, 90, 91, 93, 164, 166, 167, 194, 206, 207}, $CellContext`f4 = {38, 39, 40, 49, 50, 51, 52, 53, 62, 63, 64, 73, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 184, 193, 194, 195, 204, 205, 206, 207, 208, 217, 218, 219}, $CellContext`pRow[ Pattern[$CellContext`p, Blank[]]] := Part[$CellContext`e8b, $CellContext`p, $CellContext`sets + 6], $CellContext`rot\[Theta][ Pattern[$CellContext`\[Theta], Blank[]], Pattern[$CellContext`hp, Blank[List]]] := RotationMatrix[$CellContext`\[Theta], $CellContext`hp], \ $CellContext`dla[ Pattern[$CellContext`l, Blank[]]] := Module[{$CellContext`i = $CellContext`zeros}, Part[$CellContext`i, $CellContext`l] = 1; $CellContext`i], $CellContext`zeros := Array[0& , $CellContext`dims], $CellContext`specialFct = 1500., $CellContext`noDups[ Pattern[$CellContext`in, Blank[]]] := If[ ListQ[$CellContext`in], DeleteDuplicates[ DeleteDuplicates[$CellContext`in], If[#2 == {}, True, MemberQ[ Permutations[#2], #]]& ], 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{8, 0, 0}}, $CellContext`getNLM[ Pattern[$CellContext`p, Blank[]]] := ({$CellContext`n, $CellContext`l, $CellContext`m} = Part[$CellContext`atomList, $CellContext`p, Span[2, All]]), $CellContext`atomList = CompressedData[" 1:eJwNkWVzHDEQBWdG0t6ZmR0zU8wYM0Ni+8wcn5kZfr77Q1e/91Sl2lpVJ58S SRORb/CgKmLgGD0EU40YYjgOKeRUnOZE0iHDqWY6lSycDTnkXJzHZflQ4MwK nWkRFxbjEnoplJHL2X7hCnqlV63yKtW4BmrJdbg+iDRAozdr8qbNfFQLbqW3 QTu5g+037qR3BdXuoNKDe6GP3I8HIpFBGApmw965Ee/sj3c66p2M4XH6BPsk TJGn2WY4m8Vz9Hn2BX7GYjBZwsvcswJ/yf/YVvEafT1STUQqG3gTtsjbeCcm sgt7kdl+cO4gODsMTo+Ck2N8Qv/PfgpJ8hnbOWcX+JJ+xX7NQ9xEJrf4jnvu 4YH8yPaEn+kvMdXXmMobfocP8if+ivPG8APZ/SHd "], $CellContext`get120[ Pattern[$CellContext`p, Blank[]]] := If[ IntegerQ[ $CellContext`position[$CellContext`e8, $CellContext`p]], Ceiling[ Abs[ 121 - $CellContext`position[$CellContext`e8, $CellContext`p] - 0.1]], 120], $CellContext`count[ Pattern[$CellContext`x, Blank[List]], Pattern[$CellContext`y, Blank[]]] := Count[ N[ Round[$CellContext`x, $CellContext`cntChop]], N[ Round[$CellContext`y, $CellContext`cntChop]]], \ $CellContext`cntChop = 0.039810717055349734`, $CellContext`triListExp = {$CellContext`T1, \ $CellContext`T1p, $CellContext`T2, $CellContext`T2p, $CellContext`T4, \ $CellContext`T4p}, $CellContext`T1 = {{(-1)/2, 1/2, 1/2, (-1)/2, 0, 0, 0, 0}, {(-1)/2, 1/2, (-1)/2, 1/2, 0, 0, 0, 0}, {(-1)/2, (-1)/2, 1/2, 1/2, 0, 0, 0, 0}, {1/2, 1/2, 1/2, 1/2, 0, 0, 0, 0}, { 0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2}, { 0, 0, 0, 0, (-1)/2, 5/6, (-1)/6, (-1)/6}, { 0, 0, 0, 0, (-1)/2, (-1)/6, 5/6, (-1)/6}, { 0, 0, 0, 0, (-1)/2, (-1)/6, (-1)/6, 5/ 6}}, $CellContext`T1p = {{(-1)/2, 1/2, 1/Sqrt[2], 0, 0, 0, 0, 0}, {(-1)/2, 1/2, -(1/Sqrt[2]), 0, 0, 0, 0, 0}, {-(1/Sqrt[2]), -(1/Sqrt[2]), 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1/2, Sqrt[3]/2, 0, 0}, { 0, 0, 0, 0, -Sqrt[3]/2, 1/2, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}}, $CellContext`T2 = {{1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, -1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, { 0, 0, 0, 0, 0, -((Sqrt[3/2]/2 + 1/(2 Sqrt[6]))/Sqrt[ 6]), -((Sqrt[3/2]/2 + 1/(2 Sqrt[6]))/Sqrt[6]), Sqrt[2/3] (Sqrt[3/2]/2 + 1/(2 Sqrt[6]))}, { 0, 0, 0, 0, 0, 1/2 - (-Sqrt[3/2]/2 + 1/(2 Sqrt[6]))/Sqrt[ 6], (-1)/2 - (-Sqrt[3/2]/2 + 1/(2 Sqrt[6]))/Sqrt[6], Sqrt[2/3] (-Sqrt[3/2]/2 + 1/(2 Sqrt[6]))}, { 0, 0, 0, 0, 0, (-1)/3, 2/3, (-1)/3}}, $CellContext`T2p = {{1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1/Sqrt[2], -(1/Sqrt[2]), 0, 0, 0, 0}, { 0, 1/Sqrt[2], 1/2, 1/2, 0, 0, 0, 0}, { 0, 1/Sqrt[2], (-1)/2, (-1)/2, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}, { 0, 0, 0, 0, 0, 0, (-1)/2, -Sqrt[3]/2}, { 0, 0, 0, 0, 0, 0, Sqrt[3]/2, (-1)/2}}, $CellContext`T4 = {{(-1)/2, 1/2, 1/2, (-1)/2, 0, 0, 0, 0}, {(-1)/2, 1/2, (-1)/2, 1/2, 0, 0, 0, 0}, {(-1)/2, (-1)/2, 1/2, 1/2, 0, 0, 0, 0}, { 1/2, 1/2, 1/2, 1/2, 0, 0, 0, 0}, { 0, 0, 0, 0, (-1)/2, (-1)/2, (-1)/2, (-1)/2}, { 0, 0, 0, 0, 1/2, 1/2, (-1)/2, (-1)/2}, { 0, 0, 0, 0, 1/2, (-1)/2, 1/2, (-1)/2}, { 0, 0, 0, 0, 1/2, (-1)/2, (-1)/2, 1/2}}, $CellContext`T4p = {{(-1)/ 2, 1/2, 1/Sqrt[2], 0, 0, 0, 0, 0}, {(-1)/2, 1/2, -(1/Sqrt[2]), 0, 0, 0, 0, 0}, {-(1/Sqrt[2]), -(1/Sqrt[2]), 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, (-1)/2, -Sqrt[3]/2, 0, 0}, { 0, 0, 0, 0, Sqrt[3]/2, (-1)/2, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}}, $CellContext`noNull[ Pattern[$CellContext`in, Blank[List]]] := Module[{$CellContext`i = Length[ First[$CellContext`in]], $CellContext`tmp = DeleteCases[$CellContext`in, Alternatives[Null, {}], 2], $CellContext`out = {}}, If[$CellContext`i < 2, $CellContext`out = $CellContext`tmp, Map[If[$CellContext`i == Length[ $CellContext`noDups[#]], AppendTo[$CellContext`out, #]]& , $CellContext`tmp]]; \ $CellContext`out], $CellContext`thck = 0.001, $CellContext`numCyls = 0, $CellContext`thck2 = 0.003, $CellContext`dlPtDef = {-0.2, -1.3}, $CellContext`tipTxtMass[ Pattern[$CellContext`x, Blank[]]] := Style[ StringJoin["m=", ToString[ ScientificForm[ $CellContext`pMass[$CellContext`x], 4], FormatType -> StandardForm]], Medium], $CellContext`tipTxtLife[ Pattern[$CellContext`x, Blank[]]] := Style[ StringJoin["\[Tau]=", ToString[ ScientificForm[ $CellContext`pLife[$CellContext`x], 4], FormatType -> StandardForm]], Medium], $CellContext`cylBreakPnt = 120, $CellContext`forceCyl = False, $CellContext`centerSpin = False, $CellContext`coxeterProjTbl = {{{1/2, 0, 0, 0, 0, 0, 0, 0}, { 0, 1/2, 0, 0, 0, 0, 0, 0}, {1/2, 1/2, 0, 0, 0, 0, 0, 0}}, {{ 1/2, 1/4, (-1)/4, 0, 0, 0, 0, 0}, { 0, Sqrt[3]/4, Sqrt[3]/4, 0, 0, 0, 0, 0}, {(1/2 + Sqrt[3]/2)/ 2, (1/2 - Sqrt[3]/2)/2, (-1)/2, 0, 0, 0, 0, 0}}, {{ 1/2, 1/(2 Sqrt[2]), 0, (-1)/(2 Sqrt[2]), 0, 0, 0, 0}, { 0, 1/(2 Sqrt[2]), 1/2, 1/(2 Sqrt[2]), 0, 0, 0, 0}, { 1/Sqrt[2], (-1)/2, 0, 1/2, 0, 0, 0, 0}}, {{ 1/2, (1 + Sqrt[5])/8, (-1 + Sqrt[5])/8, (1 - Sqrt[5])/ 8, (-1 - Sqrt[5])/8, 0, 0, 0}, { 0, Sqrt[5/8 - Sqrt[5]/8]/2, Sqrt[5/8 + Sqrt[5]/8]/2, Sqrt[5/8 + Sqrt[5]/8]/2, Sqrt[5/8 - Sqrt[5]/8]/2, 0, 0, 0}, {(Sqrt[5/8 - Sqrt[5]/8] + (1 + Sqrt[5])/4)/ 2, ((1 - Sqrt[5])/4 - Sqrt[5/8 + Sqrt[5]/8])/ 2, ((1 - Sqrt[5])/4 + Sqrt[5/8 + Sqrt[5]/8])/ 2, (-Sqrt[5/8 - Sqrt[5]/8] + (1 + Sqrt[5])/4)/2, (-1)/2, 0, 0, 0}}, {{1/2, Sqrt[3]/4, 1/4, 0, (-1)/4, -Sqrt[3]/4, 0, 0}, { 0, 1/4, Sqrt[3]/4, 1/2, Sqrt[3]/4, 1/4, 0, 0}, {(1/2 + Sqrt[3]/2)/ 2, ((-1)/2 - Sqrt[3]/2)/2, 1/2, (1/2 - Sqrt[3]/2)/ 2, (1/2 - Sqrt[3]/2)/2, 1/2, 0, 0}}, {{ 1/2, Cos[Pi/7]/2, Sin[(3 Pi)/14]/2, Sin[Pi/14]/2, -Sin[Pi/14]/2, - Sin[(3 Pi)/14]/2, -Cos[Pi/7]/2, 0}, { 0, Sin[Pi/7]/2, Cos[(3 Pi)/14]/2, Cos[Pi/14]/2, Cos[Pi/14]/2, Cos[(3 Pi)/14]/2, Sin[Pi/7]/2, 0}, {(Cos[Pi/7] + Sin[Pi/7])/ 2, (-Cos[(3 Pi)/14] - Sin[(3 Pi)/14])/ 2, (Cos[Pi/14] + Sin[Pi/14])/2, (-Cos[Pi/14] + Sin[Pi/14])/ 2, (Cos[(3 Pi)/14] - Sin[(3 Pi)/14])/2, (Cos[Pi/7] - Sin[Pi/7])/ 2, (-1)/2, 0}}, {{ 1/2, Cos[Pi/8]/2, 1/(2 Sqrt[2]), Sin[Pi/8]/2, 0, -Sin[Pi/8]/ 2, (-1)/(2 Sqrt[2]), -Cos[Pi/8]/2}, { 0, Sin[Pi/8]/2, 1/(2 Sqrt[2]), Cos[Pi/8]/2, 1/2, Cos[Pi/8]/2, 1/( 2 Sqrt[2]), Sin[Pi/8]/2}, {(Cos[Pi/8] + Sin[Pi/8])/ 2, -(1/Sqrt[2]), (Cos[Pi/8] + Sin[Pi/8])/2, (-1)/ 2, (Cos[Pi/8] - Sin[Pi/8])/2, 0, (-Cos[Pi/8] + Sin[Pi/8])/2, 1/ 2}}, {{1/2, 1/4, (-1)/4, (-1)/2, (-1)/4, 1/4, 0, 0}, { 0, Sqrt[3]/4, Sqrt[3]/4, 0, -Sqrt[3]/4, -Sqrt[3]/4, 0, 0}, {((-1)/2 - Sqrt[3]/2)/2, ((-1)/2 + Sqrt[3]/2)/2, 1/ 2, ((-1)/2 - Sqrt[3]/2)/2, ((-1)/2 + Sqrt[3]/2)/2, 1/2, 0, 0}}, {{ 1/2, 1/(2 Sqrt[2]), 0, (-1)/(2 Sqrt[2]), 1/2, (-1)/(2 Sqrt[2]), 0, 1/(2 Sqrt[2])}, { 0, 1/(2 Sqrt[2]), 1/2, 1/(2 Sqrt[2]), 0, (-1)/(2 Sqrt[2]), (-1)/ 2, (-1)/(2 Sqrt[2])}, {-(1/Sqrt[2]), 1/2, 0, (-1)/ 2, -(1/Sqrt[2]), (-1)/2, 0, 1/2}}, {{(1 - Sqrt[3])/2, 0, 1/2, 1/ 2, 0, 0, 0, 0}, {0, (-1 + Sqrt[3])/2, (-1)/2, 1/2, 0, 0, 0, 0}, { 1, 0, ((-1)/2 + Sqrt[3])/2, ((-1)/2 + Sqrt[3])/2, 0, 0, 0, 0}}, {{-0.18479253090409503`, 0.18479253090409517`, -0.06417777247591215, 1, -0.3472963553338604, 0.3472963553338602, 0, 0}, { 0.6840402866513372, 0.6840402866513374, 0, 0, 0.23756469845553865`, 0.23756469845553885`, 0.3639702342662021, 0.3639702342662021}, {-0.18479253090409503`, 0.18479253090409517`, -0.06417777247591215, 1, -0.3472963553338604, 0.3472963553338602, 0, 0}}, {{ 0.594095480117793, 0.392376873691752, 0.193033322933216, 0.107623126308248, 0.0940954801177932, -0.455898878992783, -0.416640120683195, \ -0.232292081242804}, {-0.0940954801177932, 0.455898878992783, 0.416640120683195, 0.232292081242804, 0.594095480117793, 0.392376873691752, 0.193033322933216, 0.107623126308248}, {-(1/Sqrt[2]), 1/2, 0, (-1)/ 2, -(1/Sqrt[2]), (-1)/2, 0, 1/2}}, {{ 1/2, (-1)/4, 1/(2 Sqrt[2]), 1/(4 Sqrt[2]), 0, 0, (-1)/(2 Sqrt[2]), (-1)/(4 Sqrt[2])}, { 0, 0, 1/(2 Sqrt[2]), 1/(4 Sqrt[2]), 1/2, 1/4, 1/(2 Sqrt[2]), 1/(4 Sqrt[2])}, {-(1/Sqrt[2]), (-1)/(2 Sqrt[2]), 1/2, 1/4, 0, 0, (-1)/ 2, (-1)/4}}, {{ 0, -0.5567934404522487, 0.1969492517703763, -0.1969492517703763, 0.08054772639440973, -0.38529087617102353`, 0, 0.38529087617102353`}, { 0.18091315553621942`, 0, 0.16021295504274685`, 0.16021295504274685`, 0, 0.09901705165447641, 0.7663604248754179, 0.09901705165447641}, { 0, -0.08054772639440973, -0.1969492517703763, 0.1969492517703763, 0.5567934404522487, 0.38529087617102353`, 0, -0.38529087617102353`}}, {{ 1/Sqrt[2], 1/Sqrt[2], 0, 0, 0, 0, 0, 0}, {-(1/Sqrt[2]), 1/Sqrt[2], 0, 0, 0, 0, 0, 0}, { 1/Sqrt[2], -(1/Sqrt[2]), 0, 0, 0, 0, 0, 0}}, {{ 1/Sqrt[3], 1/Sqrt[3], 1/Sqrt[3], 0, 0, 0, 0, 0}, {-(1/Sqrt[2]), 0, 1/Sqrt[2], 0, 0, 0, 0, 0}, {-(1/Sqrt[2]), 0, 1/Sqrt[2], 0, 0, 0, 0, 0}}, {{ 1/2, 1/2, 1/2, 1/2, 0, 0, 0, 0}, {(-3)/(2 Sqrt[5]), (-1)/(2 Sqrt[5]), 1/(2 Sqrt[5]), 3/(2 Sqrt[5]), 0, 0, 0, 0}, { 3/(2 Sqrt[5]), 1/(2 Sqrt[5]), (-1)/(2 Sqrt[5]), (-3)/(2 Sqrt[5]), 0, 0, 0, 0}}, {{ 1/Sqrt[5], 1/Sqrt[5], 1/Sqrt[5], 1/Sqrt[5], 1/Sqrt[5], 0, 0, 0}, {-Sqrt[2/5], -(1/Sqrt[10]), 0, 1/Sqrt[10], Sqrt[2/5], 0, 0, 0}, {-Sqrt[2/5], -(1/Sqrt[10]), 0, 1/Sqrt[10], Sqrt[2/5], 0, 0, 0}}, {{ 1/Sqrt[6], 1/Sqrt[6], 1/Sqrt[6], 1/Sqrt[6], 1/Sqrt[6], 1/Sqrt[6], 0, 0}, {-Sqrt[5/14], (-3)/Sqrt[70], -(1/Sqrt[70]), 1/Sqrt[70], 3/ Sqrt[70], Sqrt[5/14], 0, 0}, { Sqrt[5/14], 3/Sqrt[70], 1/Sqrt[70], -(1/Sqrt[70]), (-3)/Sqrt[ 70], -Sqrt[5/14], 0, 0}}, {{ 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 1/Sqrt[7], 0}, {(-3)/(2 Sqrt[7]), -(1/Sqrt[7]), (-1)/(2 Sqrt[7]), 0, 1/(2 Sqrt[7]), 1/Sqrt[7], 3/(2 Sqrt[7]), 0}, {(-3)/(2 Sqrt[7]), -(1/Sqrt[7]), (-1)/(2 Sqrt[7]), 0, 1/(2 Sqrt[7]), 1/ Sqrt[7], 3/(2 Sqrt[7]), 0}}}, $CellContext`coxSubs = { "D+1=BC2", "D+1=BC3", "D+1=BC4", "D+1=BC5", "D+1=BC6", "D+1=BC7", "D+1=BC8", "A5(6)", "A7(8)", "E6(12)", "E7(18)", "20", "24", "E8(30)", "Pascal2", "Pascal3", "Pascal4", "Pascal5", "Pascal6", "Pascal7"}, $CellContext`doParticle := Module[{$CellContext`p0$, $CellContext`p1$, $CellContext`c1$}, \ $CellContext`spList = { Overscript["L", "\[Vee]"], Overscript["R", "\[Wedge]"], Overscript["L", "\[Wedge]"], Overscript["R", "\[Vee]"]}; $CellContext`p0$ = Part[$CellContext`flavorListStr, $CellContext`r1$$ = \ $CellContext`position[$CellContext`flavorRows, $CellContext`r0$$], If[$CellContext`r1$$ == 1, $CellContext`c0$$ = "w"]; If[ And[ And[$CellContext`r1$$ > 1, $CellContext`r1$$ < 5], Or[$CellContext`c0$$ == "w", $CellContext`c0$$ == "\" \""]], $CellContext`c0$$ = "r"]; If[$CellContext`r1$$ == 5, $CellContext`c0$$ = "\" \""]; $CellContext`c1$ = If[ Or[$CellContext`c0$$ == "w", $CellContext`c0$$ == "\" \""], 1, $CellContext`position[$CellContext`colorList, \ $CellContext`c0$$] - 5]; $CellContext`ptype$$, $CellContext`g0$$ = If[$CellContext`r1$$ > 2, 0, If[ And[$CellContext`r1$$ < 3, $CellContext`g0$$ == 0], 1, $CellContext`g0$$]]; If[$CellContext`r1$$ > 2, $CellContext`c1$, $CellContext`g0$$]]; $CellContext`s1$$ = If[$CellContext`r1$$ == 3, Part[$CellContext`spList, 1], $CellContext`s0$$]; If[$CellContext`r1$$ == 4, If[$CellContext`s0$$ == Part[$CellContext`spList, 4], $CellContext`s0$$ = Part[$CellContext`spList, 2]]]; $CellContext`p1$ = \ $CellContext`spConv[$CellContext`anti$$, $CellContext`p0$, $CellContext`c0$$, \ $CellContext`s1$$]; If[ Or[$CellContext`localize, $CellContext`refresh$$], $CellContext`addParticles[{$CellContext`p1$}]]; Text[ Grid[{{ $CellContext`pDisp[$CellContext`p1$]}, { $CellContext`pToolTipTxt[$CellContext`p1$]}}]]], \ $CellContext`flavorRows = { "l", "q", "\[Omega]g", "\[Phi]\[CapitalPhi]", "Ex"}, $CellContext`s1$$ = "HeptaHepteHeptiHexiPentiSteriRunciCantiPentellated", \ $CellContext`doMeson := Module[{}, If[ Or[$CellContext`localize, $CellContext`refresh$$], $CellContext`addParticles[{ $CellContext`spConv[ False, $CellContext`q2a$$, $CellContext`c2a$$, \ $CellContext`s2$$], $CellContext`spConv[ True, $CellContext`q2b$$, $CellContext`c2a$$, \ $CellContext`s3$$]}]]; Column[{ Graphics3D[{ Sphere[{0.05, -0.45, 0}, 0.5], Text[ Style[ ReplaceAll[$CellContext`q2a$$, $CellContext`qConvDoAnti], 48, Bold], {0.05, -0.45, 0}], Gray, Sphere[{0.3, 0.6, 0}, 0.5], Text[ Style[ ReplaceAll[$CellContext`q2b$$, $CellContext`qConvDoAnti], 48, White, Bold], {0.3, 0.6, 0}], Opacity[0.5], Gray, Sphere[{0.15, 0, 0}, 1]}, ImageSize -> {$CellContext`imageSize, 175}, Boxed -> False], Graphics[ Scale[{ $CellContext`txt["Spin\[Dash]0 Mesons", {250, 375}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(K\), \(0\)]\)", {200, 325}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(K\), \(+\)]\)", {300, 325}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[Pi]\), \(-\)]\)", {150, 275}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[Pi]\), \(0\)]\)", {250, 260}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[Pi]\), \(+\)]\)", {350, 275}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[Eta]\), \(0\)]\)", {230, 290}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[Eta]\), \(0\)]\)'", {270, 290}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(K\), \(-\)]\)", {200, 225}], $CellContext`txt[ "\!\(\*SuperscriptBox[OverscriptBox[\(K\), \(_\)], \ \(0\)]\)", {300, 222}]}, 0.75], ImageSize -> {$CellContext`imageSize, 100}], If[$CellContext`more$$, $CellContext`qc = \ $CellContext`symQuarkContent[ "Meson", {$CellContext`q2a$$, $CellContext`q2b$$}]; Row[{ Length[$CellContext`qc], " Mesons with this quark content. These are: ", \ $CellContext`qc}], Null]}]], $CellContext`qConvDoAnti = { "BottomQuark" -> "b", "BottomQuarkBar" -> "\!\(\*OverscriptBox[\(b\), \(_\)]\)", "CharmQuark" -> "c", "CharmQuarkBar" -> "\!\(\*OverscriptBox[\(c\), \(_\)]\)", "DownQuark" -> "d", "DownQuarkBar" -> "\!\(\*OverscriptBox[\(d\), \(_\)]\)", "StrangeQuark" -> "s", "StrangeQuarkBar" -> "\!\(\*OverscriptBox[\(s\), \(_\)]\)", "TopQuark" -> "t", "TopQuarkBar" -> "\!\(\*OverscriptBox[\(t\), \(_\)]\)", "UpQuark" -> "u", "UpQuarkBar" -> "\!\(\*OverscriptBox[\(u\), \(_\)]\)"}, \ $CellContext`symQuarkContent[ Pattern[$CellContext`type, Blank[]], Pattern[$CellContext`quarks, Blank[]]] := $CellContext`noDups[ Flatten[ Map[Part[ ParticleData[$CellContext`type, "FullSymbol"], Part[ Position[ ParticleData[$CellContext`type, "QuarkContent"], #], All, 1]]& , Permutations[$CellContext`quarks]]]], $CellContext`doBaryon := Module[{}, If[ Or[$CellContext`localize, $CellContext`refresh$$], $CellContext`addParticles[{ $CellContext`spConv[ False, $CellContext`q3a$$, "r", $CellContext`s4$$], $CellContext`spConv[ False, $CellContext`q3b$$, "g", $CellContext`s5$$], $CellContext`spConv[ False, $CellContext`q3c$$, "b", $CellContext`s6$$]}]]; Column[{ Graphics3D[{ Sphere[{0, Sqrt[3]/2, 0}, 0.5], Text[ Style[ ReplaceAll[$CellContext`q3a$$, $CellContext`qConvDoAnti], 48, Bold], {0, Sqrt[3]/2, 0.2}], Sphere[{(-1)/2, 0, 0}, 0.5], Text[ Style[ ReplaceAll[$CellContext`q3b$$, $CellContext`qConvDoAnti], 48, Bold], {(-1)/2, 0, 0}], Sphere[{1/2, 0, 0}, 0.5], Text[ Style[ ReplaceAll[$CellContext`q3c$$, $CellContext`qConvDoAnti], 48, Bold], {1/2, 0, 0}], Opacity[0.5], LightGray, Sphere[{0, Sqrt[3]/6, 0}, Sqrt[3/2]]}, ImageSize -> {$CellContext`imageSize, 175}, Boxed -> False], Graphics[ Scale[{ $CellContext`txt["Spin\[Dash]1/2 Baryons", {125, 375}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalXi]\), \(-\)]\)", {100, 350}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalXi]\), \(0\)]\)", {150, 350}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalSigma]\), \(-\)]\)", {75, 313}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalLambda]\), \(0\)]\)", {125, 324}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalSigma]\), \(0\)]\)", {125, 302}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalSigma]\), \(+\)]\)", {175, 313}], $CellContext`txt["n", {100, 275}], $CellContext`txt["p", {150, 274}], $CellContext`txt["Spin\[Dash]3/2 Baryons", {375, 375}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalOmega]\), \(-\)]\)", {375, 350}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalXi]\), \(\(*\)\(-\)\)]\)", { 350, 325}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalXi]\), \(\(*\)\(0\)\)]\)", { 400, 325}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalSigma]\), \ \(\(*\)\(-\)\)]\)", {325, 300}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalSigma]\), \ \(\(*\)\(0\)\)]\)", {375, 300}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalSigma]\), \ \(\(*\)\(+\)\)]\)", {425, 300}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalDelta]\), \(-\)]\)", {300, 275}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalDelta]\), \(0\)]\)", {350, 275}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalDelta]\), \(+\)]\)", {400, 275}], $CellContext`txt[ "\!\(\*SuperscriptBox[\(\[CapitalDelta]\), \(++\)]\)", {450, 275}]}, 0.75], ImageSize -> {$CellContext`imageSize, 100}], If[$CellContext`more$$, $CellContext`qc = \ $CellContext`symQuarkContent[ "Baryon", {$CellContext`q3a$$, $CellContext`q3b$$, \ $CellContext`q3c$$}]; Row[{ Length[$CellContext`qc], " Baryons with this quark content. These are: ", \ $CellContext`qc}], Null]}]], $CellContext`doAtom := With[{$CellContext`local$ = $CellContext`localAtom}, Module[$CellContext`local$, $CellContext`param2DA := { PlotRange -> Part[$CellContext`plotRangeA, Span[1, 2]], ImageSize -> $CellContext`imageSize, Axes -> True, AxesLabel -> Part[$CellContext`axesLabelA, Span[1, 2]]}; $CellContext`param3DA := { PlotRange -> $CellContext`plotRangeA, ImageSize -> $CellContext`imageSize, Boxed -> True, Axes -> True, AxesLabel -> $CellContext`axesLabelA, FaceGrids -> All, FaceGridsStyle -> Directive[Gray, Dotted], SphericalRegion -> True, ViewPoint -> $CellContext`viewPointA, ViewVertical -> $CellContext`viewVerticalA, ViewAngle -> $CellContext`viewAngleA}; $CellContext`z1[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`z, Blank[]]] := ReplaceAll[$CellContext`x, { Condition[71, $CellContext`z == 5] -> 57, Condition[103, $CellContext`z == 6] -> 89}]; $CellContext`z2[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]], Pattern[$CellContext`z, Blank[]]] := ReplaceAll[ Part[$CellContext`posA, $CellContext`z, $CellContext`y, 1], { Condition[71, And[$CellContext`z == 5, $CellContext`x == 71]] -> 57, Condition[103, And[$CellContext`z == 6, $CellContext`x == 103]] -> 89}]; $CellContext`plotRangeA := {{-7.5 + $CellContext`dx, 1.5 + $CellContext`dx}, {-3.5, 4.5}, {0, 1 + Max[8, If[$CellContext`stowe$$, $CellContext`n0$$ + \ ($CellContext`n0$$ - 1) (($CellContext`explode$$ - 1)/2), $CellContext`n0$$ + 3 $CellContext`explode$$]]}}; $CellContext`coords3A[ Pattern[$CellContext`y$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := Table[ Flatten[{ Mean[ Part[ $CellContext`coords2A[$CellContext`y$], $CellContext`i, All, 1]], Mean[ Part[ $CellContext`coords2A[$CellContext`y$], $CellContext`i, All, 2]], If[$CellContext`stowe$$, $CellContext`z$ + ($CellContext`z$ - \ ($CellContext`y$ + 3)/4) (($CellContext`explode$$ - 1)/ 2), $CellContext`z$ + ($CellContext`y$ - 1) $CellContext`explode$$]}], {$CellContext`i, Length[ $CellContext`coords2A[$CellContext`y$]]}]; $CellContext`gOut = If[$CellContext`view3D$$, Graphics3D[{ Table[{ EdgeForm[Black], Part[$CellContext`clrA, $CellContext`y], If[$CellContext`density$$, Inset[ $CellContext`getGraphic[ $CellContext`getNLM[ $CellContext`z1[$CellContext`x, $CellContext`z]], \ $CellContext`orb3D], Part[ $CellContext`coords3A[$CellContext`y, $CellContext`z], \ $CellContext`z1[$CellContext`x, $CellContext`z] - \ $CellContext`z2[$CellContext`x, $CellContext`y, $CellContext`z] + 1] + {$CellContext`dx, 0, 0}], $CellContext`squ[Part[ $CellContext`coords3A[$CellContext`y, $CellContext`z], \ $CellContext`z1[$CellContext`x, $CellContext`z] - \ $CellContext`z2[$CellContext`x, $CellContext`y, $CellContext`z] + 1] + {$CellContext`dx, 0, 0}, 0.8, 3]]}, {$CellContext`z, 1, $CellContext`n0$$}, {$CellContext`y, Length[ Part[$CellContext`posA, $CellContext`z]]}, \ {$CellContext`x, Part[$CellContext`posA, $CellContext`z, $CellContext`y, 1], Part[$CellContext`posA, $CellContext`z, $CellContext`y, 2]}], Table[ With[{$CellContext`x0$ = $CellContext`z1[$CellContext`x, \ $CellContext`z]}, EventHandler[{ If[$CellContext`density$$, Red, Black], Text[ Style[ Tooltip[ If[ And[$CellContext`density$$, False], " ", Row[{ Superscript["\[InvisiblePrefixScriptBase]", ElementData[$CellContext`x0$, "AtomicNumber"]], ElementData[$CellContext`x0$, "Abbreviation"]}]], Row[{ Superscript["\[InvisiblePrefixScriptBase]", ElementData[$CellContext`x0$, "AtomicNumber"]], ElementData[$CellContext`x0$, "Abbreviation"], "\[InvisiblePrefixScriptBase] ", ElementData[$CellContext`x0$, $CellContext`ttED$$]}]], Background -> If[$CellContext`density$$, LightYellow