Convex Pentagons for Edge-to-Edge Tiling, III
نویسنده
چکیده
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.
منابع مشابه
Properties of Tilings by Convex Pentagons
Let us consider an edge-to-edge and strongly balanced tiling of plane by pentagons. A node of valence s (≥3) in an edge-to-edge tiling is a point that is the common vertex of s tiles. Let W1 be a finite closed disk satisfying the property that the average valence of nodes in W1 is nearly equal to 10/3. Then, let T denote the union of the set of pentagons meeting the boundary of W1 but not conta...
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At the beginning of the series of papers we present systematic approach to exhaust the convex pentagonal tiles of edge-to-edge (EE) tilings. Our procedure is to solve the problem systematically step by step by restricting the candidates to some class. The first task is to classify both of convex pentagons and pentagonal tiling patterns. The classification of the latter is based on the analysis ...
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 32 شماره
صفحات -
تاریخ انتشار 2015