 # Square tiling

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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.

Table info: Square tiling...
Square tiling TypeRegular tiling
Vertex configuration4.4.4.4 (or 44) Face configurationV4.4.4.4 (or V44)
Schläfli symbol(s){4,4}
{}×{}
Wythoff symbol(s)4 | 2 4
Coxeter diagram(s)                                    Symmetryp4m, [4,4], (*442)
Rotation symmetryp4, [4,4]+, (442)
Dualself-dual
PropertiesVertex-transitive, edge-transitive, face-transitive
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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.