Square lattice

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 $\mathbb {Z} ^{2}$ . 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 $[4,4]$ , and orbifold notation as $*442$ .

Square lattices
Upright square Simple	diagonal square Centered

Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as the upright square lattice and diagonal square lattice; the latter is also called the centered 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.

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