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Erschienen in:
2012 | OriginalPaper | Buchkapitel
11. Symmetry Groups
verfasst von : Dr. Walter Borchardt-Ott
Erschienen in: Crystallography
Verlag: Springer Berlin Heidelberg
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Abstract
In our discussion of point and space groups, the related sub- and supergroups were mentioned without establishing that all of these are true groups in the mathematical sense. In order to show this, we will begin by showing how symmetry operations can be represented by matrices and vectors.
We will start with the symmetry operations of point groups, leaving such operations as glide planes, screw axes and translations until later.
The orientation of symmetry elements will first be described in terms of the crystallographic axes a,b,c, or a directional vector [uvw], since these are relatively easy for a beginner to understand. For example, 4c represents a 4-fold rotation axis parallel to c, while m[110] is a mirror plane normal to the [110]-direction. The symbols used in International Tables for Crystallography [16] will be also given.