Square tiling

The square tiling, or squat, is one of the three regular tilings of the Euclidean plane. 4 squares join at each vertex of this tiling. It is the only one of the three regular tilings to be self-dual. It is also the 2D hypercubic honeycomb.

Vertex coordinates
Coordinates for the vertices of a square tiling of edge length 1 are given by where i and j range over the integers.
 * $$\left(i,\,j\right),$$

Representations
A square tiling has the following Coxeter diagrams:


 * x4o4o (regular)
 * o4x4o (as rectified square tiling)
 * x4o4x (as small rhombated square tiling)
 * xØx xØx (W2|W2 symmetry, as comb product of two apeirogons)
 * s4o4o (as alternated square tiling)
 * o4s4o
 * s4o4s
 * s4x4o (as additional alternated facetings)
 * x4s4x
 * s4x4s
 * x4s4o
 * s4s4x
 * qo4oo4oq&#zx (as hull of two dual square tilings)
 * qo4xx4oq&#zx (as hull of two oopposite variant truncated square tilings)

Related polytopes
The square tiling is the colonel of a two-member regiment that also includes the square-hemiapeirogonal tiling.