{"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<p>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<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"849\" height=\"1024\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-2-849x1024.png\" alt=\"\" class=\"wp-image-5426\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-2-849x1024.png 849w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-2-414x500.png 414w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-2-1273x1536.png 1273w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-2-1698x2048.png 1698w\" sizes=\"auto, (max-width: 849px) 100vw, 849px\" \/><figcaption>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<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1574\" height=\"7917\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-6.png\" alt=\"\" class=\"wp-image-5432\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-6.png 1574w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-6-407x2048.png 407w\" sizes=\"auto, (max-width: 1574px) 100vw, 1574px\" \/><figcaption>Each of 74 concentric hulls based on 3D Norm&#8217;d vertex positions (with varying opacity in sets of 8). Vertex counts in each hull listed above.<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-7-438x1024.png\" alt=\"\" class=\"wp-image-5430\" width=\"520\" height=\"1216\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-7-438x1024.png 438w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-7-214x500.png 214w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/e8142-3d-7.png 1168w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><figcaption>9 sets of 8 concentric hulls plus the last 2 outer hulls, Vertex counts in each <br>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<p>For the sake of completeness in visualization, see below for various projections to 2D. Click these links for a higher resolution&nbsp;<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/E8-1_42_polytopes_projected_to_various_planes.png\">PNG<\/a>&nbsp;or the&nbsp;<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/E8-1_42_polytopes_projected_to_various_planes.svg\">SVG<\/a>&nbsp;version.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-Projections-2i-12c4.svg_.png\" alt=\"\" class=\"wp-image-5465\" width=\"535\" height=\"818\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-Projections-2i-12c4.svg_.png 5167w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-Projections-2i-12c4.svg_-327x500.png 327w\" sizes=\"auto, (max-width: 535px) 100vw, 535px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>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&nbsp;PNG&nbsp;or the&nbsp;SVG&nbsp;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":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5423","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=5423"}],"version-history":[{"count":11,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5423\/revisions"}],"predecessor-version":[{"id":5470,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5423\/revisions\/5470"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=5423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=5423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=5423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}