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.
Keywords
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}
}
Comments
17 pages