{"id":6527,"date":"2024-09-17T06:29:25","date_gmt":"2024-09-17T13:29:25","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=6527"},"modified":"2026-06-24T15:46:32","modified_gmt":"2026-06-24T22:46:32","slug":"the-h4-600-cell-in-all-its-beauty","status":"publish","type":"post","link":"http:\/\/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

These models use a tetrahedral mesh generator package << TetGenLink` to analyze the cells created by the edges selected. <\/p>\n\n\n\n

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

The transparent shaded blue is the outer hull that forms the Pentakis Icosidodecahedron with a vertex hull having 42 vertices of Norm=1 from the center (a combination of 30 from an IcosiDodecahedron and 12 from an Icosahedron). All 120 vertices form concentric hulls in groups:<\/p>\n\n\n\n

1) two points at the origin
2) two icosahedra (24)
3) two dodecahedra (40)
4) two larger icosahedra (24)
5) one icosidodecahedron (30)<\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

H4 600-Cell with 3D vertex shapes representing Standard Model physics particle assignments and color-coded cells<\/p>\n\n\n\n

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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

\"\"<\/a><\/figure>\n\n\n\n

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

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Same as above with interior color-coded cells displayed<\/p>\n\n\n

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3D Visualization of the outer hull of the Dual 120-Cell (600) J’ generated using T<\/em>‘<\/figcaption><\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

The Dual H4 120-cell (J’) shown above (and more below).<\/p>\n\n\n\n

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An animated alternate form 120-cell (J’), which seems to be a new (near-miss Johnson solid?) constructed using D4′ (or T’) vs. D4 (T) above.<\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

The H4 dual 120-cell (J’) build of outer edges and color-coded cells<\/p>\n\n\n\n

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The H4 dual 120-cell (J’) build of outer edges with physics particle assignments<\/p>\n\n\n\n

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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":"

These models use a tetrahedral mesh generator package << 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 … Continue reading The H4 600-Cell in all its beauty<\/span> →<\/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":[],"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