The Domino Problem of the Hyperbolic Plane for Regular Polygons

2023/02/11 by Arun Maiti, Maiti, Arun
Computer Science · Engineering · Materials Science · #Advanced Materials and Mechanics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2302.05661

openalex publication_date 2023/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℍ².

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