Rotationally Symmetric Tilings with Convex Pentagons and Hexagons

摘要

In contrast to many known results concerning periodic tilings of theEuclidean plane with pentagons, here tilings with rotational symmetry areinvestigated. A certain class of convex pentagons is introduced. It can beshown 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 abyproduct it follows that the same holds for convex hexagons.