International Tables for Crystallography

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Arithmetic crystal classes and symmorphic space groups
A. J. C. Wilson. International Tables for Crystallography (2006). Vol. C, ch. 1.4, pp. 15-22  [ doi:10.1107/97809553602060000575 ]

Abstract

Arithmetic crystal classes have four main applications in practical crystallography: in the classification of space groups; in forming symbols for certain space groups in higher dimensions; in modelling the frequency of occurrence of space groups; and in establishing `equivalent origins'. Simple descriptions and complete enumerations of the arithmetic crystal classes in one, two and three dimensions are given in this chapter. Symmorphic space groups and the effect of dispersion on diffraction symmetry are also discussed.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series 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.