Bemerkung zu der vorstehenden Arbeit yon Cli. Mauguin

On the choice of origins in the description of space groups

The set of origins available in the description of space groups is investigated with respect to equivalence. Privileged origins may be derived employing two different criteria: (i) A unique origin can be found for each short international space-group symbol by the application of simple rules (origin related to the symbol). (ii) The first standard settings of the International Tables (1952) are chosen such that the set of equivalent origins is a subset of the origins of their affine or Euclidean normalizers respectively. A list of the affine normalizers for space groups with higher than monoclinic symmetry is presented.

Opechowski-Guccione-like symbols labelling magnetic space groups independent of tabulated (0, 0, 0)+ sets

For the magnetic space-group types with a black and white lattice two sets of symbols have been proposed: the BNS symbols [Belov et al. (1957). Sov. Phys. Crystallogr. 2, 311-322] and the OG symbols [Opechowski & Guccione (1965). Magnetism, edited by G. T. Rado & H. Suhl, Vol. II, Part A, pp. 105-165. New York: Academic Press]. Whereas generators of the group can be read off the BNS symbol, International Tables for X-ray Crystallography (1952) must be consulted to interpret the OG symbols. In the cases where the black and white lattice is centred, it is shown how the OG symbols can be modified so that generators of the group can be deduced directly from the symbol.