Rotationally Symmetric Tilings with Convex Pentagons and Hexagons

2015/09/21 by Klaassen, Bernhard · 1 voice · 1 citation
#52C20 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1509.06297

Abstract

In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any given symmetry type C_n or D_n there exists a monohedral tiling generated by a pentagon from this class. For n>1 each of these tilings is also a spiral tiling with n arms. As a byproduct it follows that the same holds for convex hexagons.

Cited by

• Old problem revisited: Which equilateral convex polygons tile the plane?

Discussions

• To brighten up your Sunday morning, a tiling with rotational symmetry of order 20 made of pentagons. Constructed using ideas from Klaassen (2016) arxiv.org/pdf/1509.06297 [bsky, 8 points, 0 comments]

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