English

Semi-regular tilings of the hyperbolic plane

Combinatorics 2019-11-11 v3 Geometric Topology

Abstract

A semi-regular tiling of the hyperbolic plane is a tessellation by regular geodesic polygons with the property that each vertex has the same vertex-type, which is a cyclic tuple of integers that determine the number of sides of the polygons surrounding the vertex. We determine combinatorial criteria for the existence, and uniqueness, of a semi-regular tiling with a given vertex-type, and pose some open questions.

Keywords

Cite

@article{arxiv.1806.11393,
  title  = {Semi-regular tilings of the hyperbolic plane},
  author = {Basudeb Datta and Subhojoy Gupta},
  journal= {arXiv preprint arXiv:1806.11393},
  year   = {2019}
}

Comments

21 pages, 14 figures. Final version, to appear in Discrete Comput. Geom

R2 v1 2026-06-23T02:45:58.747Z