Rotationally Symmetric Tilings with Convex Pentagons and Hexagons

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.