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Crystallographic point groupIn crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after any of the operations in its point group. In the classification of crystals, each point group corresponds to a crystal class. There are infinitely many 3D point groups; in crystallography, however, they are restricted to be compatible with the discrete translation symmetries of a crystal lattice. This crystallographic restriction of the infinite families of general point groups results in 32 crystallographic point groups. The point group of a crystal, among other things, determines some of the crystal's optical properties, such as whether it is birefringent, or whether it shows the Pockels effect. Additional recommended knowledge
NotationThe point groups are denoted by their component symmetries. There are a few standard notations used by crystallographers, mineralogists, and physicists. For the correspondence of the two systems below, see crystal system. Schönflies notation
In Schönflies notation, point groups are denoted by a letter symbol with a subscript. The symbols used in crystallography mean the following:
Due to the crystallographic restriction theorem, n = 1, 2, 3, 4, or 6. HermannMauguin notationAn abbreviated form of the HermannMauguin notation commonly used for space groups also serves to describe crystallographic point groups. Group names are
See also


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Crystallographic_point_group". A list of authors is available in Wikipedia. 