{"id":7294,"date":"2025-09-16T12:41:47","date_gmt":"2025-09-16T19:41:47","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=7294"},"modified":"2026-01-05T08:54:19","modified_gmt":"2026-01-05T15:54:19","slug":"coxeter-sections-for-the-swirl-prism-120-diminished-rectified-600-cell","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2025\/09\/16\/coxeter-sections-for-the-swirl-prism-120-diminished-rectified-600-cell\/","title":{"rendered":"Coxeter Sections for the Swirl Prism 120-Diminished Rectified 600-Cell"},"content":{"rendered":"\n

This is an analysis of the Coxeter Sections for the Swirl Prism 120-Diminished Rectified 600-Cell. The source data, which can be found on either of two polychora sites (qfbox.info<\/a> and polytope.miraheze.org<\/a>) seems to have two missing vertices 598 as generated by their permutation lists (vs. the intended 600). The data below, with an added two vertices of {-1,-1,\u03c63<\/sup>, \u03c63<\/sup>} and {1,-1,\u03c63<\/sup>, \u03c63<\/sup>} in the suspected error sections #3 & #15, is shown in data and 3D convex hull and Coxeter sectioning forms.<\/p>\n\n\n\n

Video(s) of 4D geometry in \u201c3D Flatlander views\u201d (i.e. what it looks like if objects from 4 \u201cother\u201d dimensions pass through an area of our 3D world for a period of time<\/em><\/figcaption><\/figure>\n\n\n
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The 3D XYZ convex hull projections (with W=0) on the right and the +\/- W Coxeter Sections of the (vertex-first) rectified 600-Cell with 720 vertices on the left with framed center as subsections of sections.<\/figcaption><\/figure>\n<\/div>\n\n
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The XYZ 3D convex hull projections on the right and Coxeter Sections of the Swirl Prism 120-diminished rectified 600-Cell with 600 vertices on the left with framed center as subsections of sections.<\/figcaption><\/figure>\n<\/div>\n\n
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The Coxeter Sections for the 120 diminished vertices (i.e. the complement of the Intersection of the (vertex-first) Rectified 600-cell and the Swirl 120-Diminished Rectified 600-Cell)<\/figcaption><\/figure>\n<\/div>\n\n
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List of vertices for the Rectified 600-cell<\/figcaption><\/figure>\n<\/div>\n\n
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List of vertices for the Complement of the Intersection of the Rectified 600-cell and the Swirl 120-Diminished Rectified 600-Cell<\/figcaption><\/figure>\n<\/div>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

This is an analysis of the Coxeter Sections for the Swirl Prism 120-Diminished Rectified 600-Cell. The source data, which can be found on either of two polychora sites (qfbox.info and polytope.miraheze.org) seems to have two missing vertices 598 as generated by their permutation lists (vs. the intended 600). The data below, with an added two … Continue reading Coxeter Sections for the Swirl Prism 120-Diminished Rectified 600-Cell<\/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":[8,13,4,34,14,16],"class_list":["post-7294","post","type-post","status-publish","format-standard","hentry","category-physics","tag-3d","tag-4d","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