Teruhisa Sugimoto

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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(More)
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(More)
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(More)
I KE.LLERMEIER, H., VORBRUGG, H., and PONTOPPIDAN, K.: ’The MBB unfurlable mesh antenna (UMA) design and development’. AIAA 1 lth Communication Satellite Systems Conference, 1986, (3), pp. 8 M 6 4 2 CLARRICOATS, P. I. B., MI, z., BROWN, R. c., POULTON, G. I., and CRONE, G. E.: ‘A reconfigurable mesh reflector antenna’. IEE Conf. Publ. 1989,1, pp. 112-116 3(More)
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(More)
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