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Semi-regular Tilings of the Hyperbolic Plane

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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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Acknowledgements

The first author is supported by SERB, DST (Grant No. MTR/2017/000410). The second author acknowledges the SERB, DST (Grant No. MT/2017/000706) and the Infosys Foundation for their support. The authors are also supported by the UGC Centre for Advanced Studies. The authors thank the referee for several suggestions that significantly improved this article. Several figures in this article were made using the L2Primitives and Tess packages for Mathematica, available online at the Wolfram Library Archive.

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  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Basudeb Datta & Subhojoy Gupta

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  1. Basudeb Datta
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  2. Subhojoy Gupta
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Correspondence to Subhojoy Gupta.

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Datta, B., Gupta, S. Semi-regular Tilings of the Hyperbolic Plane. Discrete Comput Geom 65, 531–553 (2021). https://doi.org/10.1007/s00454-019-00156-0

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