{"id":3505,"date":"2015-08-27T16:06:02","date_gmt":"2015-08-27T23:06:02","guid":{"rendered":"http:\/\/theoryofeverything.org\/MyToE\/?p=3505"},"modified":"2015-12-27T18:35:10","modified_gmt":"2015-12-27T18:35:10","slug":"quasicrystals-and-geometry","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2015\/08\/27\/quasicrystals-and-geometry\/","title":{"rendered":"QuasiCrystals and Geometry"},"content":{"rendered":"<p>I found a 1995 book <a href=\"http:\/\/english.360elib.com\/datu\/Q\/EM093592.pdf\">(PDF online) &#8220;QuasiCrystals and Geometry&#8221; by Marjorie Senechal<\/a>. There were some very nice diffraction patterns that match rectified 4_21 E8 Polytope 12,18, and 30-gon projections. See my overlays below:<\/p>\n<p>12-gon Rectified E8<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3507\" rel=\"attachment wp-att-3507\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-12gon0b.png\" alt=\"quasi-Rect421-12gon0b\" width=\"500\" class=\"alignnone size-full wp-image-3507\" \/><\/a><br \/>\nDiffraction<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3506\" rel=\"attachment wp-att-3506\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-12gon1b.png\" alt=\"quasi-Rect421-12gon1b\" width=\"500\" class=\"alignnone size-full wp-image-3506\" \/><\/a><br \/>\nOverlay<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3508\" rel=\"attachment wp-att-3508\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-12gon2b.png\" alt=\"quasi-Rect421-12gon2b\" width=\"500\" class=\"alignnone size-full wp-image-3508\" \/><\/a><\/p>\n<p>18-gon Rectified E8<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3509\" rel=\"attachment wp-att-3509\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-18gon0b.png\" alt=\"quasi-Rect421-18gon0b\" width=\"500\" class=\"alignnone size-full wp-image-3509\" \/><\/a><br \/>\nDiffraction<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3527\" rel=\"attachment wp-att-3527\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-18gon1b.png\" alt=\"quasi-Rect421-18gon1b\" width=\"500\" class=\"alignnone size-full wp-image-3527\" \/><\/a><br \/>\nOverlay<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3514\" rel=\"attachment wp-att-3514\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-18gon2b.png\" alt=\"quasi-Rect421-18gon2b\" width=\"500\" class=\"alignnone size-full wp-image-3514\" \/><\/a><\/p>\n<p>30-gon Rectified E8<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3511\" rel=\"attachment wp-att-3511\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-30gon0b.png\" alt=\"quasi-Rect421-30gon0b\" width=\"500\" class=\"alignnone size-full wp-image-3511\" \/><\/a><br \/>\nDiffraction<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3510\" rel=\"attachment wp-att-3510\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-30gon1b.png\" alt=\"quasi-Rect421-30gon1b\" width=\"500\" class=\"alignnone size-full wp-image-3510\" \/><\/a><br \/>\nOverlay<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3512\" rel=\"attachment wp-att-3512\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/quasi-Rect421-30gon2b.png\" alt=\"quasi-Rect421-30gon2b\" width=\"500\" class=\"alignnone size-full wp-image-3512\" \/><\/a><\/p>\n<p>and another 12-gon rectified E8 pattern overlay from<a href=\"http:\/\/arxiv.org\/abs\/1306.3316\"> M. &#038; N. Koca&#8217;s in &#8220;12-fold Symmetric Quasicrystallography from affine E6, B6, and F4&#8221;<\/a>:<br \/>\n<a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3531\" rel=\"attachment wp-att-3531\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/koca0b.png\" alt=\"koca0b\" width=\"500\" class=\"alignnone size-full wp-image-3531\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3532\" rel=\"attachment wp-att-3532\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/koca1b.png\" alt=\"koca1b\" width=\"500\" class=\"alignnone size-full wp-image-3532\" \/><\/a><\/p>\n<p><a href=\"http:\/\/theoryofeverything.org\/MyToE\/?attachment_id=3533\" rel=\"attachment wp-att-3533\"><img decoding=\"async\" src=\"http:\/\/theoryofeverything.org\/MyToE\/wp-content\/uploads\/2015\/08\/koca2b.png\" alt=\"koca2b\" width=\"500\" class=\"alignnone size-full wp-image-3533\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I found a 1995 book (PDF online) &#8220;QuasiCrystals and Geometry&#8221; by Marjorie Senechal. There were some very nice diffraction patterns that match rectified 4_21 E8 Polytope 12,18, and 30-gon projections. See my overlays below: 12-gon Rectified E8 Diffraction Overlay 18-gon Rectified E8 Diffraction Overlay 30-gon Rectified E8 Diffraction Overlay and another 12-gon rectified E8 pattern &hellip; <a href=\"https:\/\/theoryofeverything.org\/theToE\/2015\/08\/27\/quasicrystals-and-geometry\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">QuasiCrystals and Geometry<\/span> <span class=\"meta-nav\">&rarr;<\/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":[11,4,19,34,14,35],"class_list":["post-3505","post","type-post","status-publish","format-standard","hentry","category-physics","tag-2d","tag-e8","tag-fano","tag-h4","tag-math","tag-quasicrystals"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/3505","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=3505"}],"version-history":[{"count":1,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/3505\/revisions"}],"predecessor-version":[{"id":3887,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/3505\/revisions\/3887"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=3505"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=3505"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=3505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}