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Unboundedness of the Heesch Number for Hyperbolic Convex Monotiles

Combinatorics 2026-05-19 v2

Abstract

We provide a resolution of the Heesch problem for homogeneous (also known as semi-regular) tilings, and as a corollary, for tilings by convex monotiles in the hyperbolic plane. We also provide the first known example of weakly aperiodic convex monotiles arising from the dual of homogeneous tilings.

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Cite

@article{arxiv.2603.27827,
  title  = {Unboundedness of the Heesch Number for Hyperbolic Convex Monotiles},
  author = {Arun Maiti},
  journal= {arXiv preprint arXiv:2603.27827},
  year   = {2026}
}

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17 pages