{"paper":{"title":"Fullerene-like spheres with faces of negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mathieu Dutour Sikiric, Michel Deza, Mikhail Shtogrin","submitted_at":"2011-12-14T20:15:03Z","abstract_excerpt":"Given R\\subset N, an (R,k)$-sphere is a k-regular map on the sphere whose faces have gonalities i\\in R. The most interesting/useful are (geometric) fullerenes, i.e., (\\{5,6\\},3)$-spheres.\n  Call \\kappa_i=1 + \\frac{i}{k} - \\frac{i}{2} the curvature of i-gonal faces. (R,k)-spheres admitting \\kappa_i<0 are much harder to study. We consider the symmetries and construction for three new instances of such spheres: ({a,b},k)-spheres with p_b\\le 3 (they are listed), icosahedrites (i.e., ({3,4},5)$-spheres) and, for any c\\in N, fullerene c-disks, i.e., ({5,6,c},3)-spheres with p_c=1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3320","kind":"arxiv","version":1},"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"}