The Domino Problem of the Hyperbolic Plane for Regular Polygons

Abstract

We provide a definitive classification of all finite sets of regular polygons that admit a tiling of the hyperbolic plane, thereby establishing the decidability of the Domino Problem for this class of prototiles. We show that admissibility is determined by a finite set of local and inductive combinatorial constraints. This classification further leads to the discovery of the first known examples of weakly aperiodic protosets consisting of regular polygons in ${\mathbb{H}}^2$.

The paper has been overhauled for a better presentation, the results remains the same. 27 pages, 2 figures