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.
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