Euclidean geometry | Lattice points
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 . 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. 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. (Wikipedia).
