English

Tiling with Three Polygons is Undecidable

Computational Geometry 2024-09-19 v1 Metric Geometry

Abstract

We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.

Keywords

Cite

@article{arxiv.2409.11582,
  title  = {Tiling with Three Polygons is Undecidable},
  author = {Erik D. Demaine and Stefan Langerman},
  journal= {arXiv preprint arXiv:2409.11582},
  year   = {2024}
}

Comments

17 pages, 5 figures

R2 v1 2026-06-28T18:48:25.701Z