{"paper":{"title":"Spherical tilings by congruent quadrangles over pseudo-double wheels (III) - the essential uniqueness in case of convex tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Yohji Akama, Yudai Sakano","submitted_at":"2013-12-11T03:19:15Z","abstract_excerpt":"In [B.Gruenbaum, G.C. Shephard, Spherical tilings with transitivity   properties, in: The geometric vein, Springer, New York, 1981,   pp. 65-98], they proved \"for every spherical normal tiling by  congruent tiles, if it is isohedral, then the graph is a Platonic  solid, an Archimedean dual, an n-gonal bipyramid (n>2), or an  n-gonal trapezohedron (i.e., the pseudo-double wheel of 2n  faces)\". In the classification of spherical monohedral tilings, one  naturally asks an \"inverse problem\" of their result: For a  spherical monohedral tiling of the above mentioned topologies, when is  the tiling i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3026","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"}