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.

https://arxiv.org/abs/1806.11393

h/t Henry Segerman for sharing with me.

Comments

  1. John Conway, Marek Ctrnack and I worked out most of the rules for this. I even tried for a simple motation for it all, such as 3% 3/ 9/ 2/ , but it's froghteningly complex.

    ReplyDelete
  2. wendy krieger, are the rules you worked out available somewhere for study?

    ReplyDelete
  3. Nice to see a Tyler link and know it's not completely forgotten.

    ReplyDelete
  4. We have not forgotten it at all. Brilliant peice, if i should say so.

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