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Published in:
2012 | OriginalPaper | Chapter
9. Point Groups
Author : Dr. Walter Borchardt-Ott
Published in: Crystallography
Publisher: Springer Berlin Heidelberg
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Abstract
As has been noted, the space groups of the Bravais lattices are those with the highest possible symmetry for the corresponding crystal systems. When the lattice points are now replaced by actual atoms, ions or molecules, they must themselves possess at least the full symmetry of the lattice point if the space group is to remain unchanged.
In each crystal system, only the space group of the P-lattice or, in the trigonal system the R-lattice, need be considered (see Figs. 7.7d–7.13), since the centered lattices in each system define identical points. Lattice translations, the most important of all the symmetry operations for space groups, are now discarded, and the set of symmetry elements remaining is called a point group.
The symmetry elements of these point groups and their stereographic projections are set out in Figs. 7.7e–7.13e, and the conversion from space group to point group in Table 9.1.