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Uniform tilings of the hyperbolic plane

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Uniform tilings of the hyperbolic plane
by Basudeb Datta and Subhojoy Gupta

Abstract. A uniform 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 uniform tiling with a given vertex type, and pose some open questions.

https://arxiv.org/abs/1806.11393

h/t Henry Segerman for sharing with me.

Uniform tilings of the hyperbolic plane

Image
Uniform tilings of the hyperbolic plane
by Basudeb Datta and Subhojoy Gupta

Abstract. A uniform 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 uniform tiling with a given vertex type, and pose some open questions.

https://arxiv.org/abs/1806.11393

h/t Henry Segerman for sharing with me.