{"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":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"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;\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"jgmoxness\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.8\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Visualizing a Theory of Everything! - Dedicated to the pursuit of beauty and Truth in Nature!\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!\" \/>\n\t\t<meta property=\"og:description\" content=\"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;\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2018-04-09T16:38:37+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2020-05-12T18:10:15+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!\" \/>\n\t\t<meta name=\"twitter:description\" content=\"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;\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BlogPosting\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#blogposting\",\"name\":\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!\",\"headline\":\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes\",\"author\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"publisher\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/wp-content\\\/uploads\\\/2018\\\/04\\\/E8-Projections-1d.png\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#articleImage\",\"width\":849,\"height\":1116},\"datePublished\":\"2018-04-09T09:38:37-07:00\",\"dateModified\":\"2020-05-12T11:10:15-07:00\",\"inLanguage\":\"en-US\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#webpage\"},\"isPartOf\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#webpage\"},\"articleSection\":\"Physics, E8, Math\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE#listItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"name\":\"Physics\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"position\":2,\"name\":\"Physics\",\"item\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#listItem\",\"name\":\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE#listItem\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#listItem\",\"position\":3,\"name\":\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"name\":\"Physics\"}}]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\",\"name\":\"jgmoxness\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/\",\"name\":\"jgmoxness\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#webpage\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/\",\"name\":\"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!\",\"description\":\"This is a shot of the relevant Mathematica code snippets that produce the images: E8 4_21 (with projection basis, edges, vertex overlap colors & counts) (click here for very large SVG): E8 2_41 (with projection basis, vertex overlap colors & counts) (click here for very large SVG): E8 1_42 (with projection basis,vertex overlap colors &\",\"inLanguage\":\"en-US\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#website\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2018\\\/04\\\/09\\\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\\\/#breadcrumblist\"},\"author\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"creator\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"datePublished\":\"2018-04-09T09:38:37-07:00\",\"dateModified\":\"2020-05-12T11:10:15-07:00\"},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#website\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/\",\"name\":\"Visualizing a Theory of Everything!\",\"description\":\"Dedicated to the pursuit of beauty and Truth in Nature!\",\"inLanguage\":\"en-US\",\"publisher\":{\"@id\":\"https:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!","description":"This is a shot of the relevant Mathematica code snippets that produce the images: E8 4_21 (with projection basis, edges, vertex overlap colors & counts) (click here for very large SVG): E8 2_41 (with projection basis, vertex overlap colors & counts) (click here for very large SVG): E8 1_42 (with projection basis,vertex overlap colors &","canonical_url":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BlogPosting","@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#blogposting","name":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!","headline":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes","author":{"@id":"https:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author"},"publisher":{"@id":"https:\/\/theoryofeverything.org\/theToE\/#person"},"image":{"@type":"ImageObject","url":"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2018\/04\/E8-Projections-1d.png","@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#articleImage","width":849,"height":1116},"datePublished":"2018-04-09T09:38:37-07:00","dateModified":"2020-05-12T11:10:15-07:00","inLanguage":"en-US","mainEntityOfPage":{"@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#webpage"},"isPartOf":{"@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#webpage"},"articleSection":"Physics, E8, Math"},{"@type":"BreadcrumbList","@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE#listItem","position":1,"name":"Home","item":"https:\/\/theoryofeverything.org\/theToE","nextItem":{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/#listItem","name":"Physics"}},{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/#listItem","position":2,"name":"Physics","item":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/","nextItem":{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#listItem","name":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes"},"previousItem":{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE#listItem","name":"Home"}},{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#listItem","position":3,"name":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes","previousItem":{"@type":"ListItem","@id":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/#listItem","name":"Physics"}}]},{"@type":"Person","@id":"https:\/\/theoryofeverything.org\/theToE\/#person","name":"jgmoxness"},{"@type":"Person","@id":"https:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author","url":"https:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/","name":"jgmoxness"},{"@type":"WebPage","@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#webpage","url":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/","name":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!","description":"This is a shot of the relevant Mathematica code snippets that produce the images: E8 4_21 (with projection basis, edges, vertex overlap colors & counts) (click here for very large SVG): E8 2_41 (with projection basis, vertex overlap colors & counts) (click here for very large SVG): E8 1_42 (with projection basis,vertex overlap colors &","inLanguage":"en-US","isPartOf":{"@id":"https:\/\/theoryofeverything.org\/theToE\/#website"},"breadcrumb":{"@id":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/#breadcrumblist"},"author":{"@id":"https:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author"},"creator":{"@id":"https:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author"},"datePublished":"2018-04-09T09:38:37-07:00","dateModified":"2020-05-12T11:10:15-07:00"},{"@type":"WebSite","@id":"https:\/\/theoryofeverything.org\/theToE\/#website","url":"https:\/\/theoryofeverything.org\/theToE\/","name":"Visualizing a Theory of Everything!","description":"Dedicated to the pursuit of beauty and Truth in Nature!","inLanguage":"en-US","publisher":{"@id":"https:\/\/theoryofeverything.org\/theToE\/#person"}}]},"og:locale":"en_US","og:site_name":"Visualizing a Theory of Everything! - Dedicated to the pursuit of beauty and Truth in Nature!","og:type":"article","og:title":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!","og:description":"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;","og:url":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/","article:published_time":"2018-04-09T16:38:37+00:00","article:modified_time":"2020-05-12T18:10:15+00:00","twitter:card":"summary","twitter:title":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes - Visualizing a Theory of Everything!","twitter:description":"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;"},"aioseo_meta_data":{"post_id":"5067","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"limit_modified_date":false,"created":"2022-04-06 04:23:13","updated":"2025-06-10 15:51:18"},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/theoryofeverything.org\/theToE\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/\" title=\"Physics\">Physics<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tE8 (2_41, 4_21, and 1_42) projected to various Coxeter planes\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"https:\/\/theoryofeverything.org\/theToE"},{"label":"Physics","link":"https:\/\/theoryofeverything.org\/theToE\/topics\/physics\/"},{"label":"E8 (2_41, 4_21, and 1_42) projected to various Coxeter planes","link":"https:\/\/theoryofeverything.org\/theToE\/2018\/04\/09\/e8-2_41-4_21-and-1_42-projected-to-various-coxeter-planes\/"}],"_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}]}}