3-uniform Tiling
A ''k''-uniform tiling is a tiling of Tessellation, 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 #Higher k-uniform tilings, up to ''k''=6. 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 Euclidean tilings by convex regular polygons#Tilings that are not edge-to-edge, tilings of regular polygons that are not edge-to-edge allow different sized polygons, and continuous shifting positions of contact. Classification Such periodic tilings of convex polygons may be classified by the ...
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