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On symmetry classes of crystal structures

Acta Cryst. (2009). A65, 456–465 (

[ReO3] The structures of AuCu3 (top) and ReO3 (bottom) lead to the same symmetry class but represent two different structure types.
The paper deals with an open-ended classification scheme for crystal structures based on classes of Wyckoff positions (Wyckoff sets) by special supergroups of the space groups (affine normalizers). These classes are free of metrical and geometrical considerations. The multiplicities of Wyckoff positions used in a structure description are added up and lead to a number of sites for atoms. Wyckoff sets combined with these numbers lead to classes of crystal structures. A symmetry class of crystal structures contains all members of a structure type, example cf. figure.
H. Burzlaff and H. Zimmermann