{"paper":{"title":"Quaternionic Representation of Snub 24-Cell and its Dual Polytope Derived From E_8 Root System","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":"2009-06-11T14:00:23Z","abstract_excerpt":"Vertices of the 4-dimensional semi-regular polytope,\n  \\textit{snub 24-cell} and its symmetry group $W(D_{4}):C_{3} $ of order 576 are represented in terms of quaternions with unit norm. It follows from the icosian representation of \\textbf{$E_{8} $} root system. The quaternionic root system of $H_{4} $ splits as the vertices of 24-cell and the \\textit{snub 24-cell} under the symmetry group of the \\textit{snub 24-cell} which is one of the maximal subgroups of the group \\textbf{$W(H_{4})$} as well as $W(F_{4})$. It is noted that the group is isomorphic to the\\textbf{}semi-direct product of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2109","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"}