In mathematics, the **square lattice** is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as **Z***2*. It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group in IUC notation as p4m, Coxeter notation as, and orbifold notation as *442.

Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as "upright square lattice" and "diagonal square lattice". They differ by an angle of 45°. This is related to the fact that a square lattice can be partitioned into two square sub-lattices, as is evident in the colouring of a checkerboard.

### Famous quotes containing the word square:

“Interpreting the dance: young women in white dancing in a ring can only be virgins; old women in black dancing in a ring can only be witches; but middle-aged women in colors, *square* dancing...?”

—Mason Cooley (b. 1927)