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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2012, Volume 9, Pages 478–530
(Mi semr381)
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This article is cited in 1 scientific paper (total in 1 paper)
Geometry and topology
Convex pentagons which tile the plane (types: 11112, 11122)
O. G. Bagina Kemerovo State University
Abstract:
We consider the problem of classifying the convex pentagons that tile the plane edge-to-edge. It is proved that in each such tiling of the plane by pentagons, there exists a tile whose set of vertex degrees can be one of the following: (3,3,3,3,3), (3,3,3,3,4), (3,3,3,3,5), (3,3,3,3,6), (3,3,3,4,4). This provides the possibility of searching which finally leads to exhaustive classification of such pentagons. We consider convex pentagons types 11112, 11122.
Keywords:
convex pentagon, tiling the plane, plane.
Received May 25, 2012, published November 5, 2012
Citation:
O. G. Bagina, “Convex pentagons which tile the plane (types: 11112, 11122)”, Sib. Èlektron. Mat. Izv., 9 (2012), 478–530
Linking options:
https://www.mathnet.ru/eng/semr381 https://www.mathnet.ru/eng/semr/v9/p478
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Abstract page: | 364 | Full-text PDF : | 125 | References: | 39 |
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