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Convex Pentagons for Edge-to-Edge Tiling, II

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Abstract

Based on Bagina’s Proposition, it has previously been demonstrated that there remain 34 cases where it is uncertain whether a convex pentagon can generate an edge-to-edge tiling. In this paper, these cases are further refined by imposing extra edge conditions. To investigate the resulting 42 cases, the properties of convex pentagonal tiles that can generate an edge-to-edge tiling are identified. These properties are the key to generating a perfect list of the types of convex pentagonal tiles that can generate an edge-to-edge tiling.

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Authors and Affiliations

  1. The Interdisciplinary Institute of Science, Technology and Art, Suzukidaini-building 211, 2-5-28 Kitahara, Asaka-shi, Saitama, 351-0036, Japan

    Teruhisa Sugimoto

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  1. Teruhisa Sugimoto
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Correspondence to Teruhisa Sugimoto.

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Sugimoto, T. Convex Pentagons for Edge-to-Edge Tiling, II. Graphs and Combinatorics 31, 281–298 (2015). https://doi.org/10.1007/s00373-013-1385-x

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  • DOI: https://doi.org/10.1007/s00373-013-1385-x

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