On the choice of origins in the description of space groups

Abstract

AbstractThe 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.