Exhaustive search of convex pentagons which tile the plane

2017/08/01 by Michaël Rao, Rao, Michael · 1 citation
Engineering · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1708.00274

openalex publication_date 2017/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an exhaustive search of all families of convex pentagons which tile the plane. This research shows that there are no more than the already 15 known families. In particular, this implies that there is no convex polygon which allows only non-periodic tilings.

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• Tilings of the Sphere by Congruent Pentagons I: Edge Combinations a²b²c and a³bc

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