Tiling with Three Polygons is Undecidable

EasyChair Preprint 15503

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.

Keyphrases: computability, reduction, tiling

@booklet{EasyChair:15503,
  author    = {Erik D. Demaine and Stefan Langerman},
  title     = {Tiling with Three Polygons is Undecidable},
  howpublished = {EasyChair Preprint 15503},
  year      = {EasyChair, 2024}}