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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Zn, is the lattice in the Euclidean space Rn whose 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. The integer lattice is an odd unimodular lattice.The automorphism group (or group of congruences) of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order 2n n!. As a matrix group it is given by the set of all n×n signed permutation matrices.In coarse geometry, the integer lattice is coarsely equivalent to Euclidean space.