{"id":4765,"date":"2017-10-17T14:16:08","date_gmt":"2017-10-17T21:16:08","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=4765"},"modified":"2017-10-18T13:31:19","modified_gmt":"2017-10-18T20:31:19","slug":"rotating-6d-d6-to-3d-pentagon-centered-h3-for-2d-decagon-symmetry","status":"publish","type":"post","link":"http:\/\/theoryofeverything.org\/theToE\/2017\/10\/17\/rotating-6d-d6-to-3d-pentagon-centered-h3-for-2d-decagon-symmetry\/","title":{"rendered":"Rotating 6D D6 to 3D Pentagon Centered H3 for 2D Decagon Symmetry"},"content":{"rendered":"<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-2D.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4766\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-2D.png\" alt=\"\" width=\"563\" height=\"563\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-2D.png 563w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-2D-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-2D-500x500.png 500w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4767\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3.png\" alt=\"\" width=\"563\" height=\"564\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3.png 563w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/E8-Pentagon-Center-D6-to-H3-500x500.png 500w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/a><br \/>\nInterestingly, these 2D and 3D projections includes all 240 vertices and 6720 edges of E8 with the same 2D and 3D projection. Only the vertex and edge overlap are different.<\/p>\n<p>The D6 to H3 projection based on 3 rows of the E8 to H4+H4 Phi folding matrix.<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/09\/projection1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4515\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/09\/projection1.png\" alt=\"\" width=\"137\" height=\"75\" \/><\/a><\/p>\n<p>The rotation off of the D6 to H3 projection based on the E8 to H4+H4 Phi folding matrix is<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/Decagonal-Projection.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4768\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/Decagonal-Projection.png\" alt=\"\" width=\"1075\" height=\"243\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/Decagonal-Projection.png 1075w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/Decagonal-Projection-500x113.png 500w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/Decagonal-Projection-1024x231.png 1024w\" sizes=\"auto, (max-width: 1075px) 100vw, 1075px\" \/><\/a><\/p>\n<p>Using this rotated basis, we now show rectified D6 (Cantellated 6-Orthoplex t0,2{3,3,3,3,3,4})<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outE8-d6-rect10.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4773\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outE8-d6-rect10.png\" alt=\"\" width=\"563\" height=\"564\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outE8-d6-rect10.png 563w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outE8-d6-rect10-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outE8-d6-rect10-500x500.png 500w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/a><\/p>\n<p>Bi-rectified D6<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outD6-rect20.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4778\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outD6-rect20.png\" alt=\"\" width=\"2188\" height=\"2189\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outD6-rect20.png 2188w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outD6-rect20-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outD6-rect20-500x500.png 500w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/outD6-rect20-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p>6-Orthoplex<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O0.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4780\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O0.png\" alt=\"\" width=\"2188\" height=\"2189\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O0.png 2188w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O0-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O0-500x500.png 500w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O0-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p>Rectified 6-Orthoplex (D6)<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect10.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4781\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect10.png\" alt=\"\" width=\"2188\" height=\"2189\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect10.png 2188w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect10-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect10-500x500.png 500w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect10-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p>Bi-Rectified 6-Orthoplex<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect20.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4782\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect20.png\" alt=\"\" width=\"2188\" height=\"2189\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect20.png 2188w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect20-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect20-500x500.png 500w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect20-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p>Tri-Rectified 6-Orthoplex<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect30.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4785\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect30.png\" alt=\"\" width=\"2188\" height=\"2189\" srcset=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect30.png 2188w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect30-150x150.png 150w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect30-500x500.png 500w, http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/out6O-rect30-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Interestingly, these 2D and 3D projections includes all 240 vertices and 6720 edges of E8 with the same 2D and 3D projection. Only the vertex and edge overlap are different. The D6 to H3 projection based on 3 rows of the E8 to H4+H4 Phi folding matrix. The rotation off of the D6 to H3 &hellip; <a href=\"http:\/\/theoryofeverything.org\/theToE\/2017\/10\/17\/rotating-6d-d6-to-3d-pentagon-centered-h3-for-2d-decagon-symmetry\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Rotating 6D D6 to 3D Pentagon Centered H3 for 2D Decagon Symmetry<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[4,34],"class_list":["post-4765","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-h4"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"Interestingly, these 2D and 3D projections includes all 240 vertices and 6720 edges of E8 with the same 2D and 3D projection. 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