International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 48

Let be a period lattice in with matrix A, and let be the lattice reciprocal to , with period matrix . Let be defined similarly, and let us suppose that is a sublattice of , i.e. that as a set.
The relation between and may be described in two different fashions: (i) multiplicatively, and (ii) additively.