Symmetry operation - Revision history

BrianMcMahon at 09:18, 20 November 2017

2017-11-20T09:18:54Z

BrianMcMahon: Tidied translations.

2017-11-20T09:18:42Z

Tidied translations.

BrianMcMahon at 15:54, 21 September 2017

2017-09-21T15:54:51Z

BrianMcMahon: Style edits to align with printed edition

2017-05-17T11:57:18Z

Style edits to align with printed edition

MassimoNespolo: link

2016-11-24T13:46:12Z

link

MassimoNespolo: lang

2015-03-20T04:09:26Z

lang

MassimoNespolo: Precision

2014-12-03T04:48:25Z

Precision

MassimoNespolo at 09:59, 11 May 2007

2007-05-11T09:59:11Z

New page

A '''symmetry operation''' is an '''isometry''', ''i''.''e''. a transformation under which two objects, or two configurations or an object, are brought to coincide. A symmetry operation is a [[Euclidean mapping]]: to each point of the first configuration there corresponds a point of the second configuration, the distances between two points are kept by the transformation, as are the angles.

The two configurations/objects can be either congruent or enantiomorphous. Correspondingly, the symmetry operations are classed into two kinds:
* '''symmetry operations of first kind''': they relate congruent objects and consist of translations, rotations and screw rotations;
* '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exist a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in Hermann-Mauguin notation.

A symmetry operation is performed about a [[symmetry element]].

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 09:18, 20 November 2017
Line 1:		Line 1:
−	<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrieoperation</font> (''Ge''). <font color="black">Operazione di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja'').	+	<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrieoperation</font> (''Ge''). <font color="black">Operazione di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja''). <font color="green">Operación de simetría</font> (''Sp'').
−	<font color="green">Operación de simetría</font> (''Sp'').

← Older revision		Revision as of 09:18, 20 November 2017
Line 1:		Line 1:
−	<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrieoperation</font> (''Ge''). <font color="~~green~~">~~Operación de simetría~~</font> (''Sp''). <font color="~~black~~">~~Operazione di simmetria~~</font> (''It''). <font color="~~purple~~">~~対称操作~~</font> (''Ja'').	+	<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrieoperation</font> (''Ge''). <font color="black">Operazione di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja'').
		+	<font color="green">Operación de simetría</font> (''Sp'').

← Older revision		Revision as of 15:54, 21 September 2017
Line 1:		Line 1:
−	<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">~~Symmetrie-Operationen~~ </font> (''Ge''). <font color="green">Operación de simetría</font> (''Sp''). <font color="black">~~Ooerazione~~ di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja'').	+	<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrieoperation</font> (''Ge''). <font color="green">Operación de simetría</font> (''Sp''). <font color="black">Operazione di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja'').

@@ Line 1: / Line 1: @@
-<font color="blue">Opération de symétrie</font> (''Fr''); <font color="red">Symmetrie-Operationen </font> (''Ge''); <font color="green">Operación de simetría</font> (''Sp''); <font color="black">Ooerazione di simmetria</font> (''It''); <font color="purple">対称操作</font> (''Ja'').
+<font color="blue">Opération de symétrie</font> (''Fr''). <font color="red">Symmetrie-Operationen </font> (''Ge''). <font color="green">Operación de simetría</font> (''Sp''). <font color="black">Ooerazione di simmetria</font> (''It''). <font color="purple">対称操作</font> (''Ja'').
-A '''symmetry operation''' is an '''isometry''', ''i''.''e''. a transformation under which two objects, or two configurations or an object, are brought to coincide. A symmetry operation is a [[Euclidean mapping]]: to each point of the first configuration there corresponds a point of the second configuration, the distances between two points are kept by the transformation, as are the angles.
+A '''symmetry operation''' is an '''isometry''', ''i''.''e''. a transformation under which two objects, or two configurations or an object, are brought to coincide. A symmetry operation is a [[Euclidean mapping]]: to each point of the first configuration there corresponds a point of the second configuration. The distances between two points are kept by the transformation, as are the angles.
 The two configurations/objects can be either congruent or enantiomorphous. Correspondingly, the symmetry operations are classed into two kinds:
 * '''symmetry operations of first kind''': they relate congruent objects and consist of translations, rotations and screw rotations;
-* '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exist a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in [[Hermann-Mauguin symbols|Hermann-Mauguin]] notation.
+* '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exists a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in [[Hermann-Mauguin symbols|Hermann-Mauguin]] notation.
 A symmetry operation can be performed about a [[symmetry element]]. Exceptions are the identity and the pure translations, for which a symmetry element is not defined.
 [[Category:Fundamental crystallography]]

← Older revision		Revision as of 04:09, 20 March 2015
Line 1:		Line 1:
		+	<font color="blue">Opération de symétrie</font> (''Fr''); <font color="red">Symmetrie-Operationen </font> (''Ge''); <font color="green">Operación de simetría</font> (''Sp''); <font color="black">Ooerazione di simmetria</font> (''It''); <font color="purple">対称操作</font> (''Ja'').
		+
		+
	A '''symmetry operation''' is an '''isometry''', ''i''.''e''. a transformation under which two objects, or two configurations or an object, are brought to coincide. A symmetry operation is a [[Euclidean mapping]]: to each point of the first configuration there corresponds a point of the second configuration, the distances between two points are kept by the transformation, as are the angles.		A '''symmetry operation''' is an '''isometry''', ''i''.''e''. a transformation under which two objects, or two configurations or an object, are brought to coincide. A symmetry operation is a [[Euclidean mapping]]: to each point of the first configuration there corresponds a point of the second configuration, the distances between two points are kept by the transformation, as are the angles.

@@ Line 5: / Line 5: @@
 * '''symmetry operations of second kind''': they relate enantiomorphous objects and consist of inversion, reflections, rotoinversions, and glide reflections. There exist a 1:1 correspondence between rotoinversion and rotoreflections: the latter are more used in Schoenflies notation, whereas rotoinversions are preferred in Hermann-Mauguin notation.
-A symmetry operation is performed about a [[symmetry element]].
+A symmetry operation can be performed about a [[symmetry element]]. Exceptions are the identity and the pure translations, for which a symmetry element is not defined.
 [[Category:Fundamental crystallography]]