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arXiv · 1509.06297

Rotationally Symmetric Tilings with Convex Pentagons and Hexagons

Bernhard Klaassen
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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 $\mathbf{C}_{n}$ or $\mathbf{D}_{n}$ 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.

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Bernhard Klaassen. 2015-09-21. Rotationally Symmetric Tilings with Convex Pentagons and Hexagons. https://doi.org/10.4171/em%2F310

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