Convex pentagons and concave octagons that can form rotationally symmetric tilings

2020/05/18 by Teruhisa Sugimoto, Sugimoto, Teruhisa
Engineering · Materials Science · #05B45 #52C20 #Advanced Materials and Mechanics #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2005.08470

openalex publication_date 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study, the properties of convex pentagons that can form rotationally symmetric edge-to-edge tilings are discussed. Because the rotationally symmetric tilings are formed by concave octagons that are generated by two convex pentagons connected through a line symmetry, they are considered to be equivalent to rotationally symmetric tilings with concave octagons. In addition, under certain circumstances, tiling-like patterns with a regular polygonal hole at the center can be formed using these convex pentagons.

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