Square tiling

It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex.

There are 9 distinct uniform colorings of a square tiling.

This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol {n,4}, and Coxeter diagram , with n progressing to infinity.

Isohedral tilings have identical faces (face-transitivity) and vertex-transitivity, there are 18 variations, with 6 identified as triangles that do not connect edge-to-edge, or as quadrilateral with two collinear edges.

There are 3 regular complex apeirogons, sharing the vertices of the square tiling.

An isogonal variation with two types of faces, seen as a snub square tiling with trangle pairs combined into rhombi.
Topological square tilings can be made with concave faces and more than one edge shared between two faces. This variation has 3 edges shared.
A 2-isohedral variation with rhombic faces