“Tiling With 3 Polygons Is Undecidable”, Erik D. Demaine, Stefan Langerman2024-09-17 (computability)⁠:

We prove that the following problem is co-RE-complete and thus undecidable:

given 3 simple polygons, is there a tiling of the plane where every tile is an isometry of one of the 3 polygons (either allowing or forbidding reflections)?

This result improves on the best previous construction which requires 5 polygons.