{"paper":{"title":"Grand Antiprism and Quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mehmet Koca, Mudhahir Al-Ajmi, Nazife Ozdes Koca","submitted_at":"2009-06-11T14:26:36Z","abstract_excerpt":"Vertices of the 4-dimensional semi-regular polytope, the\n  \\textit{grand antiprism} and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the \\textbf{$E_{8} $} root system which decomposes into two copies of the root system of $H_{4} $. The symmetry of the \\textit{grand antiprism} is a maximal subgroup of the Coxeter group $W(H_{4})$. It is the group $Aut(H_{2} \\oplus H'_{2})$ which is constructed in terms of 20 quaternionic roots of the Coxeter diagram $H_{2} \\oplus H'_{2}$. The root system of $H_{4} $ represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2117","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}