{"id":5513,"date":"2020-05-21T15:32:54","date_gmt":"2020-05-21T22:32:54","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=5513"},"modified":"2020-05-21T19:01:24","modified_gmt":"2020-05-22T02:01:24","slug":"3d-visualization-of-the-rays-of-e6-e7-in-kochen-specker-theory-by-ruuge-waegell-aravind","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2020\/05\/21\/3d-visualization-of-the-rays-of-e6-e7-in-kochen-specker-theory-by-ruuge-waegell-aravind\/","title":{"rendered":"3D Visualization of the rays of E6 & E7 in Kochen-specker theory by Ruuge & Waegell\/Aravind"},"content":{"rendered":"\n

In several papers on BKS proofs, Arthur Ruuge’s “Exceptional and Non-Crystallograpic Root Systems and the Kochen-Specker Theorem” https:\/\/arxiv.org\/abs\/0906.2696v1<\/a> and Mordecai Waegell & P.K. Aravind’s “Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8” https:\/\/arxiv.org\/abs\/1502.04350v2<\/a>, in addition to E8, E6 and E7 is studied. Using the visualization developed for my recent paper<\/a> and prior papers, I present here the related visualizations for E6 and E7 as discussed in those papers.<\/p>\n\n\n\n

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The 72 E6 vertices derived from E8 and projected to 3D using the “E8->H4” basis vectors. The 15*72=1080 edges are shown in the upper left, the 36 anti-podal rays are shown in the upper right along with the hull group vertex counts and norm distance. The bottom image shows the 4 hulls – yellow Icosahedron (12), cyan dodecahedron (20) and the orange\/pink pentagonal prisms (40)).<\/figcaption><\/figure>\n\n\n\n
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The 126 E7 vertices derived from E8 and projected to 3D using the “E8->H4” basis vectors. The 16*126=2016 edges are shown in the upper left, the 63 anti-podal rays are shown in the upper right along with the hull group vertex counts and norm distance. The bottom image shows the 4 hulls – orange 2 overlapping Icosahedrons (24), pink2 overlapping dodecahedron (40), and cyan & gray icosidodecahedrons(60) with 2 vertices at the origin.<\/figcaption><\/figure>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

In several papers on BKS proofs, Arthur Ruuge’s “Exceptional and Non-Crystallograpic Root Systems and the Kochen-Specker Theorem” https:\/\/arxiv.org\/abs\/0906.2696v1 and Mordecai Waegell & P.K. Aravind’s “Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8” https:\/\/arxiv.org\/abs\/1502.04350v2, in addition to E8, E6 and E7 is studied. Using the visualization developed for my recent paper and … Continue reading 3D Visualization of the rays of E6 & E7 in Kochen-specker theory by Ruuge & Waegell\/Aravind<\/span> →<\/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":[14,16],"class_list":["post-5513","post","type-post","status-publish","format-standard","hentry","category-physics","tag-math","tag-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=5513"}],"version-history":[{"count":8,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5513\/revisions"}],"predecessor-version":[{"id":5528,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5513\/revisions\/5528"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=5513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=5513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=5513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}