In geometry, the demiregular tilings are a set of Euclidean tessellations made from 2 or more regular polygon faces.
A more systematic approach looking at symmetry orbits are the 2-uniform tilings of which there are 20.
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.
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.