The eighty-one types of isohedral tilings in the plane

Abstract

1. A tiling is a collection = {Ti|i = 1, 2, …} of closed topological discs which covers the Euclidean plane E2, and of which the individual tiles Ti have disjoint interiors. We shall assume throughout that the intersection of any two tiles is a connected set. If each tile is congruent (directly or reflectively isometric) to a given set T, then the tiling is called monohedral and T is called the prototile of . Clearly every monohedral tiling is locally finite.