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Crystallographic basis

A basis of n vectors e1e2, ... , en of the  vector  space Vn is a crystallographic basis of the vector lattice L if every  integral linear combination  t = u1e1 + u2e2 + ... + unen is a lattice vector of L. It may or may not be a primitive basis.

See also

Sections 8.1 and 9.1 of International Tables of Crystallography, Volume A