Graphs and Combinatorics

, Volume 31, Issue 1, pp 281–298

Convex Pentagons for Edge-to-Edge Tiling, II

Original Paper

DOI: 10.1007/s00373-013-1385-x

Cite this article as:
Sugimoto, T. Graphs and Combinatorics (2015) 31: 281. doi:10.1007/s00373-013-1385-x

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.

Keywords

Convex pentagon Tiling Tile Monohedral tiling Edge-to-edge tiling 

Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.The Interdisciplinary Institute of Science, Technology and ArtAsaka-shiJapan

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