Geometric element

From Online Dictionary of Crystallography

Élément géométrique (Fr). Geometrische Element (Ge). Elemento geometrico (It). 幾何的要素 (Ja). Elemento geométrico (Sp).

A geometric element is an element in space (plane, line, point, or a combination of these) about which a symmetry operation is performed. Geometric elements are classified on the basis of the dimensionality N of the space on which they act, the upper limit on the dimensionality of the symmetry element being N-1.

In one-dimensional spaces N-1 = 0 and the only geometric element is a point. In two-dimensional spaces N-1 = 1 and we have points and lines. In three-dimensional spaces N-1 = 2 and we have points, lines and planes. In four-dimensional spaces N-1 = 3 and we have points, lines, planes and hyperplanes.

See also

  • Symmetry element
  • Section 1.2.3 of International Tables for Crystallography, Volume A, 6th edition


Wolff, P. M. de, Billiet, Y., Donnay, J. D. H., Fischer, W., Galiulin, R. B., Glazer, A. M., Senechal, M., Shoemaker, D. P., Wondratschek, H., Hahn, Th., Wilson, A. J. C. and Abrahams, S. C. (1989). Acta Cryst. A45, 494−499. Definition of symmetry elements in space groups and point groups. Report of the International Union of Crystallography Ad-hoc Committee on the Nomenclature of Symmetry