{"id":7779,"date":"2026-02-13T13:48:57","date_gmt":"2026-02-13T20:48:57","guid":{"rendered":"https:\/\/theoryofeverything.org\/theToE\/?p=7779"},"modified":"2026-02-15T08:29:27","modified_gmt":"2026-02-15T15:29:27","slug":"hypercomplex-e8-as-it-relates-to-the-sedenions-trigintaduonions-and-beyond","status":"publish","type":"post","link":"https:\/\/theoryofeverything.org\/theToE\/2026\/02\/13\/hypercomplex-e8-as-it-relates-to-the-sedenions-trigintaduonions-and-beyond\/","title":{"rendered":"Hypercomplex E8 as it relates to the Sedenions, Trigintaduonions, and beyond"},"content":{"rendered":"\n<p>This post will document some work I am doing related to E8, H4, and the hypercomplex forms of algebras and groups. So stay tuned&#8230;.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Cayley-Dickson Algebras to Grasmannians.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Cayley-Dickson Algebras to Grasmannians.svg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Hypercomplex numbers<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Trigintaduonions.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Trigintaduonions.svg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Trigintaduonions derived using repeated Cayley-Dickson doubling of my &#8220;Palindromic Octonions&#8221; (one of 480 possible) that creates a unique Derivation chart (as shown below).  Red are the Octonion triads and Blue are Sedenions.<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Sexagintaquatronions.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Sexagintaquatronions.svg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Sexagintaquatronions derived using repeated Cayley-Dickson doubling of my &#8220;Palindromic Octonions&#8221; (one of 480 possible) that creates a unique Derivation chart (as shown below). Red are the Octonion triads, Blue are Sedenion, and Green are Trigintaduonions.<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/palindromic-octonion-split-fano4.svg\" target=\"_blank\" rel=\" noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/palindromic-octonion-split-fano4.svg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Palindromic Octonions (with 7 split forms) and their Cayley-Dickson generated Sedenions with uniquely symmetric Derivation chart and 84 Zero Divisors <\/figcaption><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>This post will document some work I am doing related to E8, H4, and the hypercomplex forms of algebras and groups. So stay tuned&#8230;.<\/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":[4,34,14,16],"class_list":["post-7779","post","type-post","status-publish","format-standard","hentry","category-physics","tag-e8","tag-h4","tag-math","tag-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/7779","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=7779"}],"version-history":[{"count":8,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/7779\/revisions"}],"predecessor-version":[{"id":7794,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/7779\/revisions\/7794"}],"wp:attachment":[{"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=7779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=7779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=7779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}