User:Harry Princeton/List of k-uniform tilings
From Wikipedia, the free encyclopedia
A k-co-uniform tiling is a tiling of tilings of the plane by convex coregular polygons, connected edge-to-edge, with k types of dual polygons. The (1) co-uniform tiling include 3 co-regular tilings, and 8 semicoregular tilings. A co-uniform tiling can be defined by its face configuration. Higher k-co-uniform tilings are listed by their vertex figures, but are not generally uniquely identified this way.
![]() 1-uniform (regular) |
![]() 1-uniform (semiregular) |
![]() 2-uniform tiling |
![]() 3-uniform tiling |
The complete lists of k-uniform tilings have been enumerated up to k=6. There are 20 2-co-uniform tilings, 61 3-co-uniform tilings, 151 4-co-uniform tilings, 332 5-co-uniform tilings, and 673 6-co-uniform tilings. This article lists all solutions up to k=5.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Halfshift_square_tiling.svg/640px-Halfshift_square_tiling.svg.png)
Other tilings of regular polygons that are not edge-to-edge allow different sized polygons, and continuous shifting positions of contact.