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In mathematics, the ''n''-dimensional integer lattice (or cubic lattice), denoted Z''n'', is the lattice in the Euclidean space R''n'' whose lattice points are ''n''-tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. Z''n'' is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice. ==Automorphism group== 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 2''n'' ''n'' : where the symmetric group ''S''''n'' acts on (Z2)''n'' by permutation (this is a classic example of a wreath product). For the square lattice, this is the group of the square, or the dihedral group of order 8; for the three-dimensional cubic lattice, we get the group of the cube, or octahedral group, of order 48. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「integer lattice」の詳細全文を読む スポンサード リンク
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