{"id":4595,"date":"2017-10-02T13:14:14","date_gmt":"2017-10-02T20:14:14","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=4595"},"modified":"2017-10-24T16:32:43","modified_gmt":"2017-10-24T23:32:43","slug":"the-many-concentric-symmetries-of-e8-folding-including-5-cube-to","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2017\/10\/02\/the-many-concentric-symmetries-of-e8-folding-including-5-cube-to\/","title":{"rendered":"More Symmetries of E8 folding, including 5-Cube and 4-Cube (Tesseract)"},"content":{"rendered":"

The same 3 (projection basis vectors that produce the H3 Icosadodecahedron from D6 and the Rhombic Triacontahedron from the 6-Cube (or 2 sets from the 128 1\/2 Integer BC8 vertices of E8) form lower dimensional objects within E8.<\/p>\n

For more information on the above symmetries, see this post<\/a>.<\/p>\n

The 3D object identification has been confirmed by …<\/p>\n

32 vertex 5-Cube with 80 5D Norm’d Unit Length Edges
\nProjection Basis Vectors {x,y,z}:
\n\"\"<\/a><\/p>\n

Projected Vertex Data:
\n\"\"<\/a><\/p>\n

3D Rhombic 20-Hedron Outer Hull of 22 Vertices<\/p>\n

\"\"<\/a>
\nThe edge coloring on these projections are defined by which of the 6 dimensional axis the edge aligns with.<\/p>\n

10 Interrior Vertices with 10 Edges
\n\"\"<\/a>
\nAll Vertices in 3D<\/p>\n

\"\"<\/a><\/p>\n

2D faces
\n\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

16 vertex 4-Cube with 32 4D Norm’d Unit Length Edges
\nProjection Basis Vectors {x,y,z}:
\n\"\"<\/a><\/p>\n

Projected Vertex Data:
\n\"\"<\/a><\/p>\n

3D Rhombic Dodecahedron with 2 Interior Vertices<\/p>\n

\"\"<\/a><\/p>\n

2D faces
\n\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

BTW – 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","protected":false},"excerpt":{"rendered":"

The same 3 (projection basis vectors that produce the H3 Icosadodecahedron from D6 and the Rhombic Triacontahedron from the 6-Cube (or 2 sets from the 128 1\/2 Integer BC8 vertices of E8) form lower dimensional objects within E8. For more information on the above symmetries, see this post. The 3D object identification has been confirmed … Continue reading More Symmetries of E8 folding, including 5-Cube and 4-Cube (Tesseract)<\/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":[4,34,14],"class_list":["post-4595","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-h4","tag-math"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4595","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=4595"}],"version-history":[{"count":5,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4595\/revisions"}],"predecessor-version":[{"id":4869,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/4595\/revisions\/4869"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=4595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=4595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=4595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}