Detecting Isohedral Polyforms with a SAT Solver

TL;DR

This paper presents a method to determine if polyforms can tile the plane isohedrally by encoding the problem as a SAT formula, enabling automated testing across various polyforms without specialized code.

Contribution

The paper introduces a general SAT-based approach for detecting isohedral tilings of polyforms, adaptable to many types without custom modifications.

Findings

Successfully encodes tiling questions as SAT formulas

Applicable to a wide range of polyforms

Integrates with existing Heesch number computation software

Abstract

I show how to express the question of whether a polyform tiles the plane isohedrally as a Boolean formula that can be tested using a SAT solver. This approach is adaptable to a wide range of polyforms, requires no special-case code for different isohedral tiling types, and integrates seamlessly with existing software for computing Heesch numbers of polyforms.