{"paper":{"title":"Growth of Face-Homogeneous Tessellations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark E. Watkins, Stephen J. Graves","submitted_at":"2017-07-11T19:38:31Z","abstract_excerpt":"A tessellation of the plane is face-homogeneous if for some integer $k\\geq3$ there exists a cyclic sequence $\\sigma=[p_0,p_1,\\ldots,p_{k-1}]$ of integers $\\geq3$ such that, for every face $f$ of the tessellation, the valences of the vertices incident with $f$ are given by the terms of $\\sigma$ in either clockwise or counter-clockwise order. When a given cyclic sequence $\\sigma$ is realizable in this way, it may determine a unique tessellation (up to isomorphism), in which case $\\sigma$ is called monomorphic, or it may be the valence sequence of two or more non-isomorphic tessellations (polymor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03443","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"}