Tiling the pentagon Original Research Article

Finite edge-to-edge tilings of a convex pentagon with convex pentagonal tiles are discussed. Such tilings that are also cubic are shown to be impossible in several cases. A finite tiling of a polygon P is equiangular if there is a 1-1 correspondence between the angles of P and the angles of each tile (both taken in clockwise cyclic order) so that corresponding angles are equal. It is shown that there is no cubic equiangular tiling of a convex pentagon and hence it is impossible to dissect a convex pentagon into pentagons directly similar to it.