Tiling with Three Polygons is Undecidable
<|reference_start|>Tiling with Three Polygons is Undecidable: 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.<|reference_end|>
@article{demaine2024tiling,
    title={Tiling with Three Polygons is Undecidable},
    author={Erik D. Demaine, Stefan Langerman},
    journal={arXiv preprint arXiv:2409.11582},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.11582},
    primaryClass={cs.CG math.MG}
}