Forma, Vol. 27 (No. 1), pp. 93-103, 2012

Convex Pentagons for Edge-to-Edge Tiling, I

Teruhisa Sugimoto

The Interdisciplinary Institute of Science, Technology and Art, Suzukidaini-building 211, 2-5-28 Kitahara, Asaka-shi, Saitama 351-0036, Japan
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(Received January 30, 2012; Accepted September 14, 2012)

Abstract. We introduce a plan toward a perfect list of convex pentagons that can tile the whole plane in edge-to-edge manner. Our strategy is based on Bagina’s Proposition, and is direct and primitive: Generating all candidates of pentagonal tiles (several hundreds in number), classify them into the known 14 types, geometrically impossible cases, the cases that do not generate an edge-to-edge pentagonal tiling, and tentatively uncertain cases. At present, still 34 uncertain cases remain, but these case will be settled in near future. Some other results are also presented.

Keywords: Convex Pentagon, Tiling, Tile, Monohedral Tiling, Edge-to-Edge Tiling

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