Regular tilings | Tessellation | Euclidean plane geometry
List of k-uniform tilings
A k-uniform tiling is a tiling of tilings of the plane by convex regular polygons, connected edge-to-edge, with k types of vertices. The 1-uniform tiling include 3 regular tilings, and 8 semiregular tilings. A 1-uniform tiling can be defined by its vertex configuration. Higher k-uniform tilings are listed by their vertex figures, but are not generally uniquely identified this way. The complete lists of k-uniform tilings have been enumerated . There are 20 2-uniform tilings, 61 3-uniform tilings, 151 4-uniform tilings, 332 5-uniform tilings, and 673 6-uniform tilings. This article lists all solutions up to k=5. Other tilings of regular polygons that are not edge-to-edge allow different sized polygons, and continuous shifting positions of contact. (Wikipedia).
