Square tiling
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Square tiling | |
---|---|
Type | Regular tiling |
Faces | squares |
Edges | Infinite |
Vertices | Infinite |
Vertex configuration | 4.4.4.4 |
Wythoff symbol | 4 | 2 4 |
Symmetry group | p4m |
Dual | Self-dual |
Properties | planar, vertex-uniform |
Vertex Figure |
In geometry, the Square tiling is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}.
The internal angle of the square is 90 degrees so four squares at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the triangular tiling and the hexagonal tiling.
There are 9 distinct vertex-uniform colorings of a square tiling. (Naming the colors by indices on the 4 squares around a vertex: 1111, 1112(i), 1112(ii), 1122, 1123(i), 1123(ii), 1212, 1213, 1234. (i) cases have simple reflection symmetry, and (ii) glide reflection symmetry.)