{"id":6079,"date":"2023-05-10T17:43:06","date_gmt":"2023-05-11T00:43:06","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=6079"},"modified":"2023-09-03T15:28:51","modified_gmt":"2023-09-03T22:28:51","slug":"a4-group-orbits-their-polytope-hulls-using-quaternions","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2023\/05\/10\/a4-group-orbits-their-polytope-hulls-using-quaternions\/","title":{"rendered":"A4 Group Orbits & Their Polytope Hulls Using Quaternions"},"content":{"rendered":"\n

Updated: 05\/11\/2023<\/p>\n\n\n\n

This post is a Mathematica evaluation of A4 Group Orbits & Their Polytope Hulls Using Quaternions and nD Weyl Orbits. This is a work-in-process, but the current results are encouraging for evaluating ToE’s.<\/p>\n\n\n\n

Please see the this PDF<\/a> or this Mathematica Notebook (.nb)<\/a> for the details.<\/p>\n\n\n\n

The paper being referenced in this analysis is here<\/a>. <\/p>\n\n\n\n

Of course, as in most cases, this capability has been incorporated into the VisibLie_E8 Demonstration codebase. See below for example screen shots:<\/p>\n\n\n\n

\"\"<\/a>
Hasse Visualization<\/figcaption><\/figure>\n\n\n\n
\"\"<\/a>
Maximal Embeddings<\/figcaption><\/figure>\n\n\n\n

This is an example .svg file output from the same interactive demonstration:<\/p>\n\n\n\n

\"\"\/<\/a>
SVG file output from the VisibLie_E8 Coxeter-Dynkin Interactive Demonstration Pane showing the OmniTruncated A4 Group Vertex Hulls<\/figcaption><\/figure>\n\n\n\n

More code and output images below:<\/p>\n\n\n

\n
\"\"\/<\/a><\/figure>\n<\/div>\n\n
\n
\"\"<\/a><\/figure>\n<\/div>\n\n
\n
\"\"<\/a><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"

Updated: 05\/11\/2023 This post is a Mathematica evaluation of A4 Group Orbits & Their Polytope Hulls Using Quaternions and nD Weyl Orbits. This is a work-in-process, but the current results are encouraging for evaluating ToE’s. Please see the this PDF or this Mathematica Notebook (.nb) for the details. The paper being referenced in this analysis … Continue reading A4 Group Orbits & Their Polytope Hulls Using Quaternions<\/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],"class_list":["post-6079","post","type-post","status-publish","format-standard","hentry","category-physics","tag-3d","tag-4d","tag-e8","tag-h4","tag-math"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6079","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=6079"}],"version-history":[{"count":23,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6079\/revisions"}],"predecessor-version":[{"id":6236,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6079\/revisions\/6236"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=6079"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=6079"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=6079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}