View source for Symmetry element

<font color="orange">عنصر التماثل</font> (''Ar''). <font color="blue">Élément de symétrie</font> (''Fr''). <font color="red">Symmetrieelement</font> (''Ge''). <font color="black">Elemento di simmetria</font> (''It''). <font color="purple">対称要素</font> (''Ja''). <font color="green">Elemento de simetría</font> (''Sp''). 


A '''symmetry element''' (of a given [[crystal pattern|crystal structure]] or object) is defined as a concept with a double meaning, namely the combination of a [[geometric element]] with the set of [[symmetry operation]]s having this geometric element in common (termed its ''element set''). Together with the identity and the translations, for which a geometric element is not defined, the element sets cover all symmetry operations.

==One-dimensional space==
The only symmetry element that exists in this space is the '''reflection point''' (mirror point).

==Two-dimensional space==
In this space, two types of symmetry elements exist:
*'''rotation points'''
*'''reflection lines''' (mirror lines)
The inversion centre (point) does not exist in spaces of even number of dimensions.

==Three-dimensional space==
In this space, three types of geometric elements exist:
*'''inversion centres'''
*'''rotation axes'''
*'''reflection planes''' (mirror planes)
For roto-inversion operations, the [[geometric element]] is a combination of a line, about which the rotation is performed, and a point ('''inversion point''') with respect to which the inversion is performed.

==See also==
*[[Geometric element]]

==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'' 

[[Category:Fundamental crystallography]]