International Tables for Crystallography

Space groups and their descriptions
B. Souvignier, H. Wondratschek, M. I. Aroyo, G. Chapuis and A. M. Glazer. International Tables for Crystallography (2015). Vol. A, ch. 1.4, pp. 42-73  [ doi:10.1107/97809553602060000922 ]


This chapter provides an introduction to the various crystallographic items used for the presentation of the symmetry data in the space-group tables of this volume. It starts with a detailed introduction to the Hermann–Mauguin symbols for space, plane and crystallographic point groups, and to their Schoenflies symbols. A description is given of the symbols of the symmetry operations applied in the volume, and their listings in the general-position and the symmetry-operations blocks. This is followed by analysis of some specific features of the symmetry-element and general-position graphical representations of space groups. Seitz symbols for crystallographic symmetry operations are discussed and illustrated, along with the so-called additional symmetry operations of space groups, which result from the periodicity of the space groups. The classification of points in direct space into general and special Wyckoff positions, and the study of their site-symmetry groups and Wyckoff multiplicities are presented in detail. In addition, more advanced topics like Wyckoff sets, eigensymmetry groups and non-characteristic orbits are treated. The final sections offer a useful introduction to two-dimensional sections and projections of space groups and their symmetry properties.

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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of eight volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.