Integer lattice
From Wikipedia, the free encyclopedia
In mathematics, The n-dimensional integer lattice, or cubic lattice, denoted Zn, is the lattice in the standard n-dimensional real inner product space, where the inner product is the dot product, and where the lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. Zn is the simplest example of a root lattice.
[edit] Automorphism group
The group of congruences of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order
- 2n n!.
For the square lattice, this is the group of the square, of order 8; for the three dimensional cubic lattice, we get the group of the cube, or octahedral group, of order 48.
