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.
Grünbaum and Shephard enumerated the full list of 20 2-uniform tilings in Tilings and patterns, 1987:
Ghyka lists 10 of them with 2 or 3 vertex types, calling them semiregular polymorph partitions.[1]
| Plate XXVII No. 12 4.6.12 3.4.6.4 | No. 13 3.4.6.4 3.3.3.4.4 | No. 13 bis. 3.4.4.6 3.3.4.3.4 | No. 13 ter. 3.4.4.6 3.3.3.4.4 | Plate XXIV No. 13 quatuor. 3.4.6.4 3.3.4.3.4 | |
| No. 14 33.42 36 | Plate XXVI No. 14 bis. 3.3.4.3.4 3.3.3.4.4 36 | No. 14 ter. 33.42 36 | No. 15 3.3.4.12 36 | Plate XXV No. 16 3.3.4.12 3.3.4.3.4 36 |
Steinhaus gives 5 examples of non-homogeneous tessellations of regular polygons beyond the 11 regular and semiregular ones.[2] (All of them have 2 types of vertices, while one is 3-uniform.)
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.