Square tiling
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 | |
|---|---|
| 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 |
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.
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