Symmetry element - Revision history

MassimoNespolo: moved from geometric element

2018-11-30T15:02:20Z

moved from geometric element

BrianMcMahon: Tidied translations.

2017-11-20T09:17:58Z

Tidied translations.

BrianMcMahon: New translations from Ulrich Mueller (Ge, Sp)

2017-09-21T15:58:45Z

New translations from Ulrich Mueller (Ge, Sp)

MassimoNespolo: Lang (Ar)

2017-09-14T09:18:41Z

Lang (Ar)

BrianMcMahon: Style edits to align with printed edition

2017-05-17T11:55:43Z

Style edits to align with printed edition

BrianMcMahon: Style edits to align with printed edition

2017-05-12T10:05:39Z

Style edits to align with printed edition

MassimoNespolo: red link fixed

2014-06-05T12:51:53Z

red link fixed

MassimoNespolo: edited after creation of the page [geometric element]

2014-06-05T12:23:24Z

edited after creation of the page [geometric element]

MassimoNespolo at 10:10, 11 May 2007

2007-05-11T10:10:57Z

New page

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.

==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: zero and one-dimensional:
*'''rotations points'''
*'''reflection lines''' (mirror lines)
The inversion centre does not exist in spaces of even number of dimensions.

==Three-dimensional space==
In this space, three types of symmetry elements exist: zero, one- and two-dimensional:
*'''inversion centres'''
*'''rotations axes'''
*'''reflection planes''' (mirror planes)

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 15:02, 30 November 2018
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	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.		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==		==See also==

← Older revision		Revision as of 09:17, 20 November 2017
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−	<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'').	+	<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.		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.

← Older revision		Revision as of 15:58, 21 September 2017
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−	<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''); <font color="~~orange~~">~~عنصر التماثل~~</font> (''Ar'').	+	<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.		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.

← Older revision		Revision as of 09:18, 14 September 2017
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−	<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'').	+	<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''); <font color="orange">عنصر التماثل</font> (''Ar'').

	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.		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.

← Older revision		Revision as of 11:55, 17 May 2017
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−	<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'').	+	<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'').

	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.		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.

@@ Line 4: / Line 4: @@
 ==See also==
-[[Geometric element]]
+*[[Geometric element]]
-==References==
+==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. & 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.
+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]]

@@ Line 1: / Line 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'').
-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.
+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.
 ==See also==