Point group
From Online Dictionary of Crystallography
Groupe ponctuel (Fr); Punktgruppe (Ge); Gruppo punto (It); 点群 (Ja).
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Definition
A point group is a group of symmetry operations all of which leave at least one point unmoved. A crystallographic point group is a point group that maps a point lattice onto itself: in three dimensions rotations and rotoinversions are restricted to 1, 2, 3, 4, 6 and 
, 
(= m), 
, 
, 
respectively.
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Occurrence
Crystallographic point groups occur:
- in vector space, as symmetries of the external shapes of crystals (morphological symmetry), as well as symmetry of the physical properties of the crystal ("vector point group");
- in point space, as site-symmetry groups of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra ("point point group").
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See also
Chapter 10 in International Tables for Crystallography, Volume A
