Journal for Geometry and Graphics 29 (2025), No. 2, 161--171
Copyright by the authors licensed under CC BY SA 4.0
Old Problem Revisited: Which Equilateral Convex Polygons Tile the Plane?
Bernhard Klaassen
Fraunhofer Research Institution IEG, Bochum, Germany
bernhard.klaassen@ieg.fraunhofer.de
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.
Keywords: Plane tiling, equilateral tiling, convex tiling.
MSC: 52C20.
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