{"id":6527,"date":"2024-09-17T06:29:25","date_gmt":"2024-09-17T13:29:25","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=6527"},"modified":"2024-11-14T08:11:42","modified_gmt":"2024-11-14T15:11:42","slug":"the-h4-600-cell-in-all-its-beauty","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2024\/09\/17\/the-h4-600-cell-in-all-its-beauty\/","title":{"rendered":"The H4 600-Cell in all its beauty"},"content":{"rendered":"\n<p>These models use a tetrahedral mesh generator package &lt;&lt; TetGenLink` to analyze the cells created by the edges selected. <\/p>\n\n\n\n<p class=\"has-text-align-center\">Note: The Mathematica auto-generated geometry statistics of 120 vertices, 720 golden-ratio length edges, 1200 faces, and 600 color-coded cells, with a surface area of 11.4 volume of 127.<\/p>\n\n\n\n<p class=\"has-text-align-center\">The transparent shaded blue is the outer hull that forms the Pentakis Icosidodecahedron with a vertex hull having 30 vertices of Norm=1 from the center. All 120 vertices form concentric hulls in groups:<\/p>\n\n\n\n<p class=\"has-text-align-center\">1) two points at the origin<br>2) two icosahedra (24)<br>3) two dodecahedra (40)<br>4) two larger icosahedra (24)<br>5) one icosidodecahedron (30)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-3D-stats.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-3D-stats.png\" alt=\"\" class=\"wp-image-6541\" style=\"width:799px;height:auto\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-3D-stats.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-3D-stats-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-3D-stats-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">H4 600-Cell with 3D vertex shapes representing Standard Model physics particle assignments  and color-coded cells<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-new5.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-new5.png\" alt=\"\" class=\"wp-image-6543\" style=\"width:800px;height:auto\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-new5.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-new5-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/600-cell-new5-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">H4 600-Cell with 1200 unit length edges, 2400 faces and 600-cells. 3D vertex shapes representing Standard Model physics particle assignments  and color-coded cells are also shown<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2q.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2q.png\" alt=\"\" class=\"wp-image-6566\" style=\"width:800px;height:auto\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2q.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2q-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2q-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">The H4 120-cell (J), dual of the 600-cell, showing the hull of the chamfered dodecahedron. It is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron. It can more accurately be called an order-5 truncated rhombic triacontahedron because only the order-5 vertices are truncated. It is shown with physics particle assignments.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2r.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2r.png\" alt=\"\" class=\"wp-image-6559\" style=\"width:800px;height:auto\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2r.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2r-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2r-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2t.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2t.png\" alt=\"\" class=\"wp-image-6570\" style=\"width:800px;height:auto\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2t.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2t-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2t-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">Same as above with interior color-coded cells displayed<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2022\/08\/T-120-cell_with_600_vertices.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"451\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2022\/08\/T-120-cell_with_600_vertices.png\" alt=\"\" class=\"wp-image-5969\" style=\"width:450px;height:auto\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2022\/08\/T-120-cell_with_600_vertices.png 450w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2022\/08\/T-120-cell_with_600_vertices-150x150.png 150w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/a><figcaption class=\"wp-element-caption\"><em>3D Visualization of the outer hull of the Dual 120-Cell (600) J&#8217; generated using T<\/em>&#8216;<\/figcaption><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-center\">The Dual H4 120-cell (J&#8217;) shown above (and more below).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-anim8.gif\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-anim8.gif\" alt=\"\" class=\"wp-image-6545\"\/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">An animated alternate form 120-cell (J&#8217;), which seems to be a new (near-miss Johnson solid?) constructed using D4&#8242; (or T&#8217;) vs. D4 (T) above.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2f.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2f.png\" alt=\"\" class=\"wp-image-6549\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2f.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2f-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2f-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">The H4 dual 120-cell (J&#8217;) build of outer edges and color-coded cells<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/outE80.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/outE80.png\" alt=\"\" class=\"wp-image-6551\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/outE80.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/outE80-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/outE80-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-align-center\">The H4 dual 120-cell (J&#8217;) build of outer edges with physics particle assignments<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2p.png\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1023\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2p.png\" alt=\"\" class=\"wp-image-6560\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2p.png 1021w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2p-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2024\/09\/120-cell-new-2p-150x150.png 150w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/a><figcaption class=\"wp-element-caption\">There is yet another construction of a 120-cell that has the same outer hull as the 600-Cell (above), yet with the 600 vertices (5 on each of the 120 vertices of the 600-Cell. The exception to this is a set of 6 square faces.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>These models use a tetrahedral mesh generator package &lt;&lt; TetGenLink` to analyze the cells created by the edges selected. Note: The Mathematica auto-generated geometry statistics of 120 vertices, 720 golden-ratio length edges, 1200 faces, and 600 color-coded cells, with a surface area of 11.4 volume of 127. The transparent shaded blue is the outer hull &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2024\/09\/17\/the-h4-600-cell-in-all-its-beauty\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">The H4 600-Cell in all its beauty<\/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":[8,4,34,14,16],"class_list":["post-6527","post","type-post","status-publish","format-standard","hentry","category-physics","tag-3d","tag-e8","tag-h4","tag-math","tag-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6527","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=6527"}],"version-history":[{"count":24,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6527\/revisions"}],"predecessor-version":[{"id":6768,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6527\/revisions\/6768"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=6527"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=6527"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=6527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}