Difference between revisions of "Geometric element"
From Online Dictionary of Crystallography
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<font color="blue">Élément géométrique</font> (''Fr''); <font color="black">Elemento geometrico</font> (''It''); <font color="purple">幾何学要素</font> (''Ja''). | <font color="blue">Élément géométrique</font> (''Fr''); <font color="black">Elemento geometrico</font> (''It''); <font color="purple">幾何学要素</font> (''Ja''). | ||
| − | A '''geometric element''' is a | + | 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. |
==One-dimensional space== | ==One-dimensional space== | ||
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==Three-dimensional space== | ==Three-dimensional space== | ||
In this space, three types of geometric elements exist: zero, one- and two-dimensional: | In this space, three types of geometric elements exist: zero, one- and two-dimensional: | ||
| − | *'''inversion centres | + | *'''inversion centres''' |
*'''rotations axes''' | *'''rotations axes''' | ||
*'''reflection planes''' (mirror planes) | *'''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== | ==See also== | ||
Revision as of 17:07, 5 June 2014
Élément géométrique (Fr); Elemento geometrico (It); 幾何学要素 (Ja).
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.
Contents
One-dimensional space
The only geometric element that exists in this space is the reflection point (mirror point).
Two-dimensional space
In this space, two types of geometric elements exist: zero and one-dimensional:
- rotations 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: zero, one- and two-dimensional:
- inversion centres
- rotations 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
References
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. & Abrahams, S. C. (1989). 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. Acta Cryst., A 45, 494−499.