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.
20 2-uniform tilings Grünbaum and Shephard enumerated the full list of 20 2-uniform tilings in Tilings and patterns, 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.
References
Ghyka, M. The Geometry of Art and Life, (1946), 2nd edition, New York: Dover, 1977. Keith Critchlow, Order in Space: A design source book, 1970, pp. 62–67 Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. pp. 35–43
Steinhaus, H. Mathematical Snapshots 3rd ed, (1969), Oxford University Press, and (1999) New York: Dover Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman. ISBN 0-7167-1193-1. p. 65 Chavey, D. (1989). "Tilings by Regular Polygons—II: A Catalog of Tilings". Computers & Mathematics with Applications. 17: 147–165. doi:10.1016/0898-1221(89)90156-9. In Search of Demiregular Tilings, Helmer Aslaksen
External links Weisstein, Eric W. "Demiregular tessellation". MathWorld. n-uniform tilings Brian Galebach