International Tables for Crystallography

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Derivation of symbols and coordinate triplets
W. Fischer and E. Koch. International Tables for Crystallography (2006). Vol. A, ch. 11.2, pp. 812-816  [ doi:10.1107/97809553602060000523 ]

Abstract

Chapter 11.2 describes a method for deriving the symbol of a symmetry operation (i.e. its type, the location of its symmetry element, and possibly its glide or screw vector) from its coordinate triplet as given in the `general position' of a space group. The reverse procedure is also explained. A table shows the coordinate triplets and the 3 × 3 matrices for all symmetry operations of crystallographic point groups and for all orientations of the corresponding symmetry elements.


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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.