{"id":4742,"date":"2017-10-09T16:58:01","date_gmt":"2017-10-09T23:58:01","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=4742"},"modified":"2020-05-12T11:01:09","modified_gmt":"2020-05-12T18:01:09","slug":"6-demicubes-to-rhombic-triacontahedron-via-h4-folding-matrix","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/09\/6-demicubes-to-rhombic-triacontahedron-via-h4-folding-matrix\/","title":{"rendered":"6  Demicubes Projected via H4 Folding Matrix"},"content":{"rendered":"<p>Taking the 32 vertex 6 Demicube with an even number of -1 elements and projecting with 3 of the 4 rows of the H4 folding matrix gives an dodecahedron hull with 12 vertices and 30 edges on the hull out of 240 edges of 6D length Sqrt[2]).<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-even-dodecahedronb.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-even-dodecahedronb.png\" alt=\"\" width=\"970\" height=\"981\" class=\"aligncenter size-full wp-image-4757\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-even-dodecahedronb.png 970w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-even-dodecahedronb-494x500.png 494w\" sizes=\"auto, (max-width: 970px) 100vw, 970px\" \/><\/a><\/p>\n<p><em><strong>BTW &#8211; if you find this information useful, or provide any portion of it to others, PLEASE make sure you cite this post. If you feel a blog post citation would not be an acceptable form for academic research papers, I would be glad to clean it up and put it into LaTex format in order to provide it to arXiv (with your academic sponsorship) or Vixra. Just send me a note at:\u00a0 jgmoxness@theoryofeverthing.org.\u00a0<\/strong><\/em><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-even.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-even.png\" alt=\"\" width=\"2188\" height=\"2189\" class=\"aligncenter size-full wp-image-4744\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-even.png 2188w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-even-150x150.png 150w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-even-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-even-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surf.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surf.png\" alt=\"\" width=\"2188\" height=\"2189\" class=\"aligncenter size-full wp-image-4746\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surf.png 2188w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surf-150x150.png 150w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surf-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surf-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p>While taking the 32 vertex 6 Demicube with odd number of -1 elements and projecting with 3 of the 4 rows of the H4 folding matrix gives the icosahedron with 20 vertices and 30 edges on the hull out of 240 edges of 6D length Sqrt[2]).<\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-odd-icosahedrona.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-odd-icosahedrona.png\" alt=\"\" width=\"1621\" height=\"1601\" class=\"aligncenter size-full wp-image-4758\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-odd-icosahedrona.png 1621w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-odd-icosahedrona-500x494.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/6demicube-odd-icosahedrona-1024x1011.png 1024w\" sizes=\"auto, (max-width: 1621px) 100vw, 1621px\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd.png\" alt=\"\" width=\"2188\" height=\"2189\" class=\"aligncenter size-full wp-image-4743\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd.png 2188w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-150x150.png 150w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surfa.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surfa.png\" alt=\"\" width=\"2188\" height=\"2189\" class=\"aligncenter size-full wp-image-4749\" srcset=\"https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surfa.png 2188w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surfa-150x150.png 150w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surfa-500x500.png 500w, https:\/\/theoryofeverything.org\/theToE\/wp-content\/uploads\/2017\/10\/demi-6-odd-surfa-1024x1024.png 1024w\" sizes=\"auto, (max-width: 2188px) 100vw, 2188px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Taking the 32 vertex 6 Demicube with an even number of -1 elements and projecting with 3 of the 4 rows of the H4 folding matrix gives an dodecahedron hull with 12 vertices and 30 edges on the hull out of 240 edges of 6D length Sqrt[2]). BTW &#8211; if you find this information useful, &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/09\/6-demicubes-to-rhombic-triacontahedron-via-h4-folding-matrix\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">6  Demicubes Projected via H4 Folding Matrix<\/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":[4,34,14,16],"class_list":["post-4742","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-h4","tag-math","tag-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4742","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=4742"}],"version-history":[{"count":5,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4742\/revisions"}],"predecessor-version":[{"id":4760,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4742\/revisions\/4760"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=4742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=4742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=4742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}