Klaassen, BernhardBernhardKlaassen2025-12-012025-12-012025https://publica.fraunhofer.de/handle/publica/49995210.48550/arXiv.2506.18473We present a simplified proof of a forty-year-old result con cerning 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.enpaper