The eighty-one types of isohedral tilings in the plane

Abstract

1. Atilingis a collection= {Ti|i= 1, 2, …} of closed topological discs which covers the Euclidean planeE2, and of which the individualtiles Tihave disjoint interiors. We shall assume throughout that the intersection of any two tiles is a connected set. If each tile iscongruent(directly or reflectively isometric) to a given setT, then the tilingis calledmonohedralandTis called theprototileof. Clearly every monohedral tiling is locally finite.