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On the Heesch number for the hyperbolic plane

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Abstract

We prove that there exists a polygon with arbitrary Heesch number on the hyperbolic plane.

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References

  1. C. Mann, “Hyperbolic regular polygons with notched edges,” Discrete Comput. Geom. 34(1), 143–166 (2005).

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  2. C. Mann, On Heesch’s Problem and Other Tiling Problems, Ph. D. Thesis (Univ. of Arkansas, Fayetteville, AR, 2001).

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  3. D. Eppstein, Heesch’s problem, http://www.ics.uci.edu/_eppstein/junkyard/heesch/.

  4. A. D. Aleksandrov, “On the tiling of space by polyhedra,” Vestnik Leningrad. Univ. Ser.Mat. Fiz. Him., No. 2, 33–43 (1954).

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Authors and Affiliations

  1. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    A. S. Tarasov

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  1. A. S. Tarasov
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Correspondence to A. S. Tarasov.

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Original Russian Text © A. S. Tarasov, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 1, pp. 97–104.

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Tarasov, A.S. On the Heesch number for the hyperbolic plane. Math Notes 88, 97–102 (2010). https://doi.org/10.1134/S0001434610070096

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  • DOI: https://doi.org/10.1134/S0001434610070096

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