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. 1.4, pp. 121122
Section 1.4.4.5. Relationships between direct and reciprocal Bravais lattices
U. Shmueli^{a}

Centred Bravais lattices in crystal space give rise to systematic absences of certain classes of reflections (IT I, 1952; IT A, 1983) and the corresponding points in the reciprocal lattice have accordingly zero weights. These absences are periodic in reciprocal space and their `removal' from the reciprocal lattice results in a lattice which – like the direct one – must belong to one of the fourteen Bravais lattice types. This must be so since the point group of a crystal leaves its lattice – and also the associated reciprocal lattice – unchanged. The magnitudes of the structure factors (the weight functions) are also invariant under the operation of this point group.
The correspondence between the types of centring in direct and reciprocal lattices is given in Table 1.4.4.1.

Notes:
References
International Tables for Crystallography (1983). Vol. A, SpaceGroup Symmetry, edited by Th. Hahn. Dordrecht: Reidel.International Tables for Xray Crystallography (1952). Vol. I, Symmetry Groups, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press.
Authier, A. (1981). The Reciprocal Lattice. Edited by the IUCr Commission on Crystallographic Teaching. Cardiff: University College Cardiff Press.
Buerger, M. J. (1942). Xray Crystallography. New York: John Wiley.