Tiling Problem of Convex Pentagon
نویسندگان
چکیده
We discovered the new tiling patterns each of which is composed of a single kind of convex pentagon. Moreover, we propose a new concept of classification method of the tessellating convex pentagons, which is the only unsolved case among the corresponding tessellating convex polygon problems.
منابع مشابه
Systematic Study of Convex Pentagonal Tilings, II: Tilings by Convex Pentagons with Four Equal-length Edges
We derived 14 types of tiling cases under a restricted condition in our previous report, which studied plane tilings with congruent convex pentagons. That condition is referred to as the category of the simplest set of node (vertex of edge-to-edge tiling) conditions when the tile is a convex pentagon with four equal-length edges. This paper shows the detailed properties of convex pentagonal til...
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It is shown that an equilateral convex pentagon tiles the plane if and only if it has two angles adding to 180 o or it is the unique equilateral convex pentagon with Although the area of mathematical tilings has been of interest for a long time there is still much to be discovered. We do not even know which convex polygons tile the plane. Furthermore, for those polygons which do tile, new tilin...
متن کاملSystematic Study of Convex Pentagonal Tilings, I: Case of Convex Pentagons with Four Equal-length Edges
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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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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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 ...
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