The 37 combinatorial types of minimal, non-transitive, equivariant tilings of the Euclidean plane

Dress A, Scharlau R. The 37 combinatorial types of minimal, non-transitive, equivariant tilings of the Euclidean plane. Discrete Mathematics. 1986;60:121-138.A tiling of the Euclidean plane is called minimal non-transitive if its symmetry group has exactly two orbits on the vertices, edges, and tiles. As an application of the method of generalized Schläfli symbols, which had been introduced in previous papers, a complete enumeration of all homeomeric types of minimal non-transitive tilings is given. Using the same method, this enumeration is easily extended to all 2-isotoxal tilings (see also [8])