# Geometric element

### From Online Dictionary of Crystallography

BrianMcMahon (Talk | contribs) (Tidied translations and added German and Spanish (U. Mueller)) |
(Text moved to symmetry element, where it actually belongs.) |
||

Line 1: | Line 1: | ||

<font color="blue">Élément géométrique</font> (''Fr''). <font color="red">Geometrische Element</font> (''Ge''). <font color="black">Elemento geometrico</font> (''It''). <font color="purple">幾何的要素</font> (''Ja''). <font color="green">Elemento geométrico</font> (''Sp''). | <font color="blue">Élément géométrique</font> (''Fr''). <font color="red">Geometrische Element</font> (''Ge''). <font color="black">Elemento geometrico</font> (''It''). <font color="purple">幾何的要素</font> (''Ja''). <font color="green">Elemento geométrico</font> (''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. | 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. | |

- | + | ||

- | + | ||

- | + | ||

- | In | + | |

- | + | ||

- | + | ||

- | + | ||

- | + | ||

- | + | ||

- | + | ||

- | + | ||

- | + | ||

- | + | ||

- | + | ||

==See also== | ==See also== |

## Latest revision as of 15:06, 30 November 2018

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

## Reference

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.* A**45**, 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*