{"id":5067,"date":"2018-04-09T09:38:37","date_gmt":"2018-04-09T16:38:37","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=5067"},"modified":"2020-05-12T11:10:15","modified_gmt":"2020-05-12T18:10:15","slug":"e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/","title":{"rendered":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes"},"content":{"rendered":"<p>This is a shot of the relevant Mathematica code snippets that produce the images:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-Projections-1d.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-5068\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-Projections-1d.png\" alt=\"\" width=\"849\" height=\"1116\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-Projections-1d.png 849w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-Projections-1d-380x500.png 380w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-Projections-1d-779x1024.png 779w\" sizes=\"auto, (max-width: 849px) 100vw, 849px\" \/><\/a><\/p>\n<p>E8 4_21 (with projection basis, edges, vertex overlap colors &amp; counts) (<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/E8-4_21_polytopes_projected_to_various_planes.svg\">click here for very large SVG<\/a>):<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5479 size-full\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1.png\" alt=\"\" width=\"1723\" height=\"2812\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1.png 1723w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1-306x500.png 306w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1-627x1024.png 627w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1-941x1536.png 941w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-4_21_polytopes_projected_to_various_planesa-1-1255x2048.png 1255w\" sizes=\"auto, (max-width: 1723px) 100vw, 1723px\" \/><\/a>E8 2_41 (with projection basis, vertex overlap colors &amp; counts) (<a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/E8-2_41_polytopes_projected_to_various_planes.svg\">click here for very large SVG<\/a>):<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5457 size-full\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb-e1589244045665.png\" alt=\"\" width=\"2068\" height=\"3866\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb-e1589244045665.png 2068w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb-e1589244045665-267x500.png 267w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb-e1589244045665-548x1024.png 548w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb-e1589244045665-822x1536.png 822w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-2_41_polytopes_projected_to_various_planesb-e1589244045665-1096x2048.png 1096w\" sizes=\"auto, (max-width: 2068px) 100vw, 2068px\" \/><\/a><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-2_41b.png\">E8 1_42 (with projection basis,vertex overlap colors &amp; counts) (<\/a><a href=\"http:\/\/theoryofeverything.org\/TOE\/JGM\/E8-1_42_polytopes_projected_to_various_planes.svg\">click here for very large SVG<\/a>):<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-Projections-2i-12c4.svg_.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-5465 size-full\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2020\/05\/E8-Projections-2i-12c4.svg_.png\" alt=\"\" width=\"5167\" height=\"7912\" 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: 5167px) 100vw, 5167px\" \/><\/a>Files of the actual vertex lists:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/images\/e8-4_21.txt\">E8-4_21.txt (240)<\/a><br \/>\n<a href=\"http:\/\/theoryofeverything.org\/images\/e8-2_41.txt\">E8-2_41.txt (2160) (EVEN +\/- signs on some vertices producing incorrect projections)<\/a><br \/>\n<a href=\"http:\/\/theoryofeverything.org\/images\/e8-1_42.txt\">E8-1_42.txt (17280)\u00a0<\/a><a href=\"http:\/\/theoryofeverything.org\/images\/e8-2_41.txt\"> (EVEN +\/- signs on some vertices producing incorrect projections)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a shot of the relevant Mathematica code snippets that produce the images: E8 4_21 (with projection basis, edges, vertex overlap colors &amp; counts) (click here for very large SVG): E8 2_41 (with projection basis, vertex overlap colors &amp; counts) (click here for very large SVG): E8 1_42 (with projection basis,vertex overlap colors &amp; &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes<\/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":[4,14],"class_list":["post-5067","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-math"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5067","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=5067"}],"version-history":[{"count":11,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5067\/revisions"}],"predecessor-version":[{"id":5480,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/5067\/revisions\/5480"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=5067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=5067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=5067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}