Difference between revisions of "Point group"
From Online Dictionary of Crystallography
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==Occurrence== | ==Occurrence== | ||
Crystallographic point groups occur: | 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; | + | * 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|site-symmetry groups]] of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra. | + | * in [[point space]], as [[site symmetry|site-symmetry groups]] of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra ("point point group"). |
==See also== | ==See also== | ||
Revision as of 16:04, 27 February 2007
Groupe ponctuel (Fr); Gruppo punto (It); 点群 (Ja).
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 [math]\bar 1[/math], [math]\bar 2[/math] (= m), [math]\bar 3[/math], [math]\bar 4[/math], [math]\bar 6[/math] respectively.
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").
See also
Chapter 10 in International Tables for Crystallography, Volume A