Old problem revisited: Which equilateral convex polygons tile the plane?

Bernhard Klaassen

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arXiv · 2506.18473

Old problem revisited: Which equilateral convex polygons tile the plane?

Bernhard Klaassen

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Abstract

We present a simplified proof of a forty-year-old result concerning the tiling of the plane with equilateral convex polygons. Our approach is based on a theorem by M. Rao, who used an exhaustive computer search to confirm the completeness of the well-known list of fifteen pentagon types. Assuming the validity of Rao's result, we provide a concise and mainly geometric proof of a tiling theorem originally due to Hirschhorn and Hunt. Finally, a possible connection to quasicrystals is sketched.

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Bernhard Klaassen. 2025-11-10. Old problem revisited: Which equilateral convex polygons tile the plane?. https://arxiv.org/abs/2506.18473

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