Difference between revisions of "Symmetry element"

Revision as of 12:23, 5 June 2014

Élément de symétrie (Fr); Elemento di simmetria (It); 対称要素 (Ja).

A symmetry element (of a given 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 operations 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.

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.

@@ Line 1: / Line 1: @@
-A [[symmetry element]] is a [[direct lattice|lattice]] element about which a [[symmetry operation]] is performed. Symmetry 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.
+<font color="blue">Élément de symétrie</font> (''Fr''); <font color="black">Elemento di simmetria</font> (''It''); <font color="purple">対称要素</font> (''Ja'').
-==One-dimensional space==
+A '''symmetry element''' (of a given [[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.
-The only symmetry element that exists in this space is the '''reflection point''' (mirror point).
-==Two-dimensional space==
+==See also==
-In this space, two types of symmetry elements exist: zero and one-dimensional:
+[[Geometric element]]
-*'''rotations points'''
-*'''reflection lines''' (mirror lines)
-The inversion centre does not exist in spaces of even number of dimensions.
-==Three-dimensional space==
+==References==
-In this space, three types of symmetry elements exist: zero, one- and two-dimensional:
+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.
-*'''inversion centres'''
-*'''rotations axes'''
-*'''reflection planes''' (mirror planes)
 [[Category:Fundamental crystallography]]

Difference between revisions of "Symmetry element"

From Online Dictionary of Crystallography

Revision as of 12:23, 5 June 2014

See also

References