Pentagon Tiling - Non-convex Pentagons

Non-convex Pentagons

With pentagons that are not required to be convex, additional types of tiling are possible. An example is the sphinx tiling, an aperiodic tiling formed by a pentagonal rep-tile (Godrèche 1989). The sphinx may also tile the plane periodically, by fitting two sphinx tiles together to form a parallelogram and then tiling the plane by translates of this parallelogram, a pattern that can also be used for certain other shapes of non-convex pentagons.