{"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":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t