![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Tiling_4a_simple.svg/640px-Tiling_4a_simple.svg.png&w=640&q=50)
Square tiling
Regular tiling of the Euclidean plane / From Wikipedia, the free encyclopedia
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille.
Square tiling | |
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Type | Regular tiling |
Vertex configuration | 4.4.4.4 (or 44)![]() |
Face configuration | V4.4.4.4 (or V44) |
Schläfli symbol(s) | {4,4} {∞}×{∞} |
Wythoff symbol(s) | 4 | 2 4 |
Coxeter diagram(s) | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry | p4m, [4,4], (*442) |
Rotation symmetry | p4, [4,4]+, (442) |
Dual | self-dual |
Properties | Vertex-transitive, edge-transitive, face-transitive |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/34/RIAN_archive_341196_Kursk_Nuclear_Power_Plant.jpg/640px-RIAN_archive_341196_Kursk_Nuclear_Power_Plant.jpg)
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.