Showing posts from July, 2018

Uniform tilings of the hyperbolic plane

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. h/t Henry Segerman for sharing with me.