{"paper":{"title":"Snub 24-Cell Derived from the Coxeter-Weyl Group W(D4)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mehmet Koca, Muataz Al-Barwani, Nazife Ozdes Koca","submitted_at":"2011-06-17T10:11:00Z","abstract_excerpt":"Snub 24-cell is the unique uniform chiral polytope in four dimensions consisting of 24 icosahedral and 120 tetrahedral cells. The vertices of the 4-dimensional semi-regular polytope snub 24-cell and its symmetry group ${(W(D_{4})\\mathord{/{\\vphantom {(W(D_{4}) C_{2}}}. \\kern-\\nulldelimiterspace} C_{2}}):S_{3} $ of order 576 are obtained from the quaternionic representation of the Coxeter-Weyl group \\textbf{$W(D_{4}).$}The symmetry group is an extension of the proper subgroup of the Coxeter-Weyl group \\textbf{$W(D_{4})$}by the permutation symmetry of the Coxeter-Dynkin diagram \\textbf{$D_{4} .$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3433","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"}