Geometric element
From Online Dictionary of Crystallography
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Élément géométrique (Fr); Elemento geometrico (It); 幾何学要素 (Ja).
A geometric element is a lattice element 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 and inversion points
- rotations axes
- reflection planes (mirror planes)
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.