Point group

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;
• in point space, as site-symmetry groups of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra.

See also

Chapter 10 in International Tables for Crystallography, Volume A