The Interdisciplinary Institute of Science, Technology and Art,
Suzukidaini-building 211, 2-5-28 Kitahara, Asaka-shi, Saitama 351-0036, Japan
E-mail address: firstname.lastname@example.org
(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