{"id":5423,"date":"2020-05-08T14:06:13","date_gmt":"2020-05-08T21:06:13","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=5423"},"modified":"2020-05-12T10:58:02","modified_gmt":"2020-05-12T17:58:02","slug":"3d-visualization-of-e8-1_42-polytope","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2020\/05\/08\/3d-visualization-of-e8-1_42-polytope\/","title":{"rendered":"3D visualization of E8 1_42 polytope"},"content":{"rendered":"\n

This is what I expect to be the first ever 3D visualization of the E8 1_42 polytope with 17280 vertices showing concentric hulls of Platonic solid related structures!<\/p>\n\n\n\n

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E8 1_42 polytope with 17280 vertices showing concentric hulls of Platonic solid related structures! Vertex colors represent the overlap counts.<\/figcaption><\/figure>\n\n\n\n
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Each of 74 concentric hulls based on 3D Norm’d vertex positions (with varying opacity in sets of 8). Vertex counts in each hull listed above.<\/figcaption><\/figure>\n\n\n\n
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9 sets of 8 concentric hulls plus the last 2 outer hulls, Vertex counts in each
of 8 hull listed above. Notice this is a combination of two overlapped dodecahedrons (40) and a Nonuniform Rhombicosidodecahedron (60).<\/figcaption><\/figure>\n\n\n\n

For the sake of completeness in visualization, see below for various projections to 2D. Click these links for a higher resolution PNG<\/a> or the SVG<\/a> version.<\/p>\n\n\n\n

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

This is what I expect to be the first ever 3D visualization of the E8 1_42 polytope with 17280 vertices showing concentric hulls of Platonic solid related structures! For the sake of completeness in visualization, see below for various projections to 2D. Click these links for a higher resolution PNG or the SVG version.<\/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":[4,14,16],"class_list":["post-5423","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-math","tag-physics"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t