Twin operation - Revision history

BrianMcMahon: Added German and Spanish translations (U. Mueller)

2017-11-20T14:21:58Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-17T14:50:49Z

Style edits to align with printed edition

MassimoNespolo at 11:16, 26 February 2007

2007-02-26T11:16:31Z

MassimoNespolo at 10:29, 26 February 2007

2007-02-26T10:29:05Z

MassimoNespolo at 09:42, 15 May 2006

2006-05-15T09:42:24Z

AndreAuthier at 16:35, 26 April 2006

2006-04-26T16:35:33Z

MassimoNespolo at 15:55, 26 April 2006

2006-04-26T15:55:29Z

MassimoNespolo: fr, it

2006-04-26T13:52:30Z

fr, it

GiovanniFerraris at 10:42, 26 April 2006

2006-04-26T10:42:29Z

New page

<Font color="black"> Operazione di geminazione </Font>(''It'')

The operation (action) of an element of symmetry that generates a ''[[twin]]''.

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 14:21, 20 November 2017
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−	<font color="blue">Opération de maclage</font> (''Fr''). <~~Font~~ color="black">Operazione di geminazione</~~Font~~> (''It''). <~~Font~~ color="purple">双晶操作</~~Font~~> (''Ja'').	+	<font color="blue">Opération de maclage</font> (''Fr''). <font color="red">Zwillingsoperation</font> (''Ge''). <font color="black">Operazione di geminazione</font> (''It''). <font color="purple">双晶操作</font> (''Ja''). <font color="green">Operación de macla</font> (''Sp'').

@@ Line 1: / Line 1: @@
-<font color="blue">Opération de maclage</font> (''Fr'');  <Font color="black">Operazione di geminazione</Font> (''It''); <Font color="purple">双晶操作</Font> (''Ja'').
+<font color="blue">Opération de maclage</font> (''Fr''). <Font color="black">Operazione di geminazione</Font> (''It''). <Font color="purple">双晶操作</Font> (''Ja'').
 The operation (action) of an element of symmetry that generates a ''[[twin]]''.
-Let H<sub>i</sub> be the oriented [[point group]] of the i-th individual of a [[twin]]. The intersection group of the oriented vector point groups H<sub>i</sub> of the individuals is indicated as H* = &cap;<sub>i</sub>H<sub>i</sub>. The symmetry of a twin is identified in [[vector space]] by a point group K which is a supergroup of H*. The [[coset]] decomposition of K with respect to H* gives the possible [[twin law]]s, each coset representing a [[twin law]], and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of H*.
+Let ''H<sub>i</sub>'' be the oriented [[point group]] of the ''i''-th individual of a [[twin]]. The intersection group of the oriented vector point groups ''H<sub>i</sub>'' of the individuals is indicated as ''H''* = &cap;<sub>''i''</sub>''H<sub>i</sub>''. The symmetry of a twin is identified in [[vector space]] by a point group ''K'' which is a supergroup of ''H''*. The [[coset]] decomposition of ''K'' with respect to ''H''* gives the possible [[twin law]]s, each coset representing a [[twin law]], and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of ''H''*.
-Operations in H describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing K in terms of H* connect the different individuals. To underline their different nature, the twin operations are often associated with a "colour" and K is a thus a chromatic vector point group, known as ''twin point group''.
+Operations in ''H'' describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing ''K'' in terms of ''H''* connect the different individuals. To underline their different nature, the twin operations are often associated with a 'colour' and ''K'' is a thus a chromatic vector point group, known as a ''twin point group''.
 == See also ==
-<br> Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>
+*Chapter 3.3 of ''International Tables for Crystallography, Volume D''
 [[Category:Twinning]]

← Older revision		Revision as of 11:16, 26 February 2007
Line 1:		Line 1:
−	<font color="blue">Opération de maclage</font> (''Fr''). <Font color="black">Operazione di geminazione</Font> (''It'')	+	<font color="blue">Opération de maclage</font> (''Fr''); <Font color="black">Operazione di geminazione</Font> (''It''); <Font color="purple">双晶操作</Font> (''Ja'').

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 The operation (action) of an element of symmetry that generates a ''[[twin]]''.
-Let H<sub>i</sub> be the oriented [[point group]] of the i-th individual of a [[twin]]. The intersection group of the oriented vector point groups H<sub>i</sub> of the individuals is indicated as H* = &cap;<sub>i</sub>H<sub>i</sub>. The symmetry of a twin is identified in [[vector space]] by a point group K which is a supergroup of H*. The [[coset decomposition]] of K with respect to H* gives the possible [[twin law]]s, each coset representing a [[twin law]], and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of H*.
+Let H<sub>i</sub> be the oriented [[point group]] of the i-th individual of a [[twin]]. The intersection group of the oriented vector point groups H<sub>i</sub> of the individuals is indicated as H* = &cap;<sub>i</sub>H<sub>i</sub>. The symmetry of a twin is identified in [[vector space]] by a point group K which is a supergroup of H*. The [[coset]] decomposition of K with respect to H* gives the possible [[twin law]]s, each coset representing a [[twin law]], and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of H*.
 Operations in H describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing K in terms of H* connect the different individuals. To underline their different nature, the twin operations are often associated with a "colour" and K is a thus a chromatic vector point group, known as ''twin point group''.

← Older revision		Revision as of 09:42, 15 May 2006
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	<br> Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>		<br> Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>

−	[[Category:~~Fundamental crystallography~~]]	+	[[Category:Twinning]]

@@ Line 8: / Line 8: @@
 Operations in H describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing K in terms of H* connect the different individuals. To underline their different nature, the twin operations are often associated with a "colour" and K is a thus a chromatic vector point group, known as ''twin point group''.
-==References==
+== See also ==
-*Chapter 3.3 of International Tables of Crystallography, Volume D
 [[Category:Fundamental crystallography]]

← Older revision		Revision as of 15:55, 26 April 2006
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	The operation (action) of an element of symmetry that generates a ''[[twin]]''.		The operation (action) of an element of symmetry that generates a ''[[twin]]''.

		+	Let H<sub>i</sub> be the oriented [[point group]] of the i-th individual of a [[twin]]. The intersection group of the oriented vector point groups H<sub>i</sub> of the individuals is indicated as H* = ∩<sub>i</sub>H<sub>i</sub>. The symmetry of a twin is identified in [[vector space]] by a point group K which is a supergroup of H. The [[coset decomposition]] of K with respect to H gives the possible [[twin law]]s, each coset representing a [[twin law]], and each operation in a coset representing a twin operation; the operations in a coset are equivalent under the operations of H*.

		+	Operations in H describe the vector point symmetry of the individuals, whereas those in the cosets obtained by decomposing K in terms of H* connect the different individuals. To underline their different nature, the twin operations are often associated with a "colour" and K is a thus a chromatic vector point group, known as ''twin point group''.
		+
		+	==References==
		+	*Chapter 3.3 of International Tables of Crystallography, Volume D

	[[Category:Fundamental crystallography]]		[[Category:Fundamental crystallography]]

← Older revision		Revision as of 13:52, 26 April 2006
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−	<Font color="black"> Operazione di geminazione </Font>(''It'')	+	<font color="blue">Opération de maclage</font> (''Fr''). <Font color="black">Operazione di geminazione</Font> (''It'')
−