Systematic Study of Convex Pentagonal Tilings, II: Tilings by Convex Pentagons with Four Equal-length Edges

Teruhisa Sugimoto¹* and Tohru Ogawa^2,3

¹The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan
²(Emeritus Professor of University of Tsukuba), 1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8577, Japan
³The Interdisciplinary Institute of Science, Technology and Art, Suzukidaini-building 211, 2-5-28 Kitahara, Asaka-shi, Saitama 351-0036, Japan
*E-mail address: ismsugi@gmail.com

(Received September 27, 2009; Accepted January 20, 2010)

Abstract. 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 tiles with four equal-length edges and tiling patterns. Furthermore, we present the relationship between the idiomatic expression in various overviews and our results.

Keywords: Convex Pentagon, Tiling, Tile, Node, Pattern