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In geometry, the demiregular tilings are a set of Euclidean tessellations made from 2 or more regular polygon faces. Different authors have listed different sets of tilings. A more systematic approach looking at symmetry orbits are the 2-uniform tilings of which there are 20. Some of the demiregular ones are actually 3-uniform tilings.
Contents
20 2-uniform tilings
Grünbaum and Shephard enumerated the full list of 20 2-uniform tilings in Tilings and Paterns, 1987:
Ghyka's list (1946)
Ghyka lists 10 of them with 2 or 3 vertex types, calling them semiregular polymorph partitions.
Steinhaus's list (1969)
Steinhaus gives 5 examples of non-homogeneous tessellations of regular polygons beyond the 11 regular and semiregular ones. (All of them have 2 types of vertices, while one is 3-uniform.)
Critchlow's list (1970)
Critchlow identifies 14 demi-regular tessellations, with 7 being 2-uniform, and 7 being 3-uniform.
He codes letter names for the vertex types, with superscripts to distinguish face orders. He recognizes A, B, C, D, F, and J can't be a part of continuous coverings of the whole plane.