Semi-regular tilings of the hyperbolic plane

2018/06/29 by Datta, Basudeb, Gupta, Subhojoy · 1 citation
#51M20 #52C20 #57M50 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1806.11393

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.

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