{"paper":{"title":"From the icosahedron to natural triangulations of $\\CC P^2$ and $S^2 \\times S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Basudeb Datta, Bhaskar Bagchi","submitted_at":"2010-04-19T11:04:30Z","abstract_excerpt":"We present two constructions in this paper: (a) A 10-vertex triangulation $\\CC P^{2}_{10}$ of the complex projective plane $\\CC P^{2}$ as a subcomplex of the join of the standard sphere ($S^{2}_4$) and the standard real projective plane ($\\RR P^{2}_{6}$, the decahedron), its automorphism group is $A_4$; (b) a 12-vertex triangulation $(S^{2} \\times S^{2})_{12}$ of $S^{2} \\times S^{2}$ with automorphism group $2S_5$, the Schur double cover of the symmetric group $S_5$. It is obtained by generalized bistellar moves from a simplicial subdivision of the standard cell structure of $S^{2} \\times S^{2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3157","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"}