{"id":2660,"date":"2015-02-25T11:27:58","date_gmt":"2015-02-25T18:27:58","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=2660"},"modified":"2015-02-25T11:27:58","modified_gmt":"2015-02-25T18:27:58","slug":"e8-h4-quasi-crystals-penrose-tiling-boerdijk-coxeter-helices-and-an-ams-blog-post-on-the-topic","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2015\/02\/25\/e8-h4-quasi-crystals-penrose-tiling-boerdijk-coxeter-helices-and-an-ams-blog-post-on-the-topic\/","title":{"rendered":"E8, H4, Quasi-Crystals, Penrose Tiling, Boerdijk-Coxeter Helices and an AMS blog post on the topic"},"content":{"rendered":"

This pic is an overlay of an image from Greg Egan on the AMS blog VisualInsight<\/a> on top of one I created several years ago for the quasicrystal wikipedia page<\/a>.<\/p>\n

It uses my E8-H4 folding matrix<\/a> to project E8 vertices to several interesting objects. The 5 dimensional 5-cube (Penteract) and the related 3D the Rhombic-Triacontahedron, as well as this 2D overlay on the Ho-Mg-Zn electron diffraction pattern.<\/p>\n

\"Ho-Mg-Zn_E8-5Cube-baez-egan-overlay\"<\/a><\/p>\n

E8 vertices projected to 2D pentagonal projection
\n\"E8-5Cube\"<\/a><\/p>\n

5-cube in 3D
\n\"5-cube-2\"<\/a><\/p>\n

6-cube edges projected to the Rhombic-Triacontahedron using 3 of 4 rows of my E8-H4 folding matrix.
\n\"6Cube-QuasiCrystal-low\"<\/a><\/p>\n

Rhombic-Triacontahedron with inner edges removed
\n\"RhombicTricontahedron\"<\/a><\/p>\n

The Boerdijk-Coxeter helix is also related to these structures through the Golden Ratio.<\/p>\n

Edges on the outer ring of the E8 Petrie projection related to Boerdijk-Coxeter helix.
\n\"helix2Db\"<\/a><\/p>\n

Same as above in 3D with the tetrahedral cell faces and 3D vertex shape-color-size based on quantum particle parameters from a theoretical physics model.
\n\"cells6004b\"<\/a><\/p>\n

Same as above also showing the inner E8 ring Boerdijk-Coxeter helix.
\n\"inner-outerP\"<\/a>
\nPlatonic solids
\n\"E8-3D-Platonic-2\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

This pic is an overlay of an image from Greg Egan on the AMS blog VisualInsight on top of one I created several years ago for the quasicrystal wikipedia page. It uses my E8-H4 folding matrix to project E8 vertices to several interesting objects. The 5 dimensional 5-cube (Penteract) and the related 3D the Rhombic-Triacontahedron, … Continue reading E8, H4, Quasi-Crystals, Penrose Tiling, Boerdijk-Coxeter Helices and an AMS blog post on the topic<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[33,24,4,34,16,35],"class_list":["post-2660","post","type-post","status-publish","format-standard","hentry","category-physics","tag-boerdijk-coxeter","tag-chemistry","tag-e8","tag-h4","tag-physics","tag-quasicrystals"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/2660","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=2660"}],"version-history":[{"count":0,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/2660\/revisions"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=2660"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=2660"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=2660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}