Noncrystallographic symmetry - Revision history

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

2017-11-16T13:12:16Z

Added German and Spanish translations (U. Mueller)

BrianMcMahon: Style edits to align with printed edition

2017-05-16T09:52:21Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ 6th edition of ITA

2017-04-10T16:19:41Z

‎See also: 6th edition of ITA

MassimoNespolo: typo in Ja

2016-11-26T22:31:36Z

typo in Ja

BrianMcMahon at 15:33, 7 January 2016

2016-01-07T15:33:20Z

MassimoNespolo: /* Discussion */ internal link to category

2015-03-30T05:52:38Z

‎Discussion: internal link to category

MassimoNespolo: /* Discussion */ precision

2015-03-30T05:50:35Z

‎Discussion: precision

MassimoNespolo: /* See also */ broken link fixed

2013-11-06T14:25:32Z

‎See also: broken link fixed

TedJanssen at 19:03, 18 May 2009

2009-05-18T19:03:13Z

TedJanssen at 19:02, 18 May 2009

2009-05-18T19:02:40Z

← Older revision		Revision as of 13:12, 16 November 2017
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−	<font color="blue">Symétrie non cristallographique</font> (''Fr''). <font color="black">Simmetria non cristallografica</font> (''It''). <font color="purple">非結晶的対称</font> (''Ja'').	+	<font color="blue">Symétrie non cristallographique</font> (''Fr''). <font color="red">Nichtkristallogtaphische Symmetrie</font> (''Ge''). <font color="black">Simmetria non cristallografica</font> (''It''). <font color="purple">非結晶的対称</font> (''Ja''). <font color="green">Simetría no cristalográfica</font> (''Sp'').

	== Definition ==		== Definition ==

@@ Line 1: / Line 1: @@
-<font color="blue">Symétrie non cristallographique</font> (''Fr''); <font color="black">Simmetria non cristallografica</font> (''It''); <font color="purple">非結晶的対称</font> (''Ja'')
+<font color="blue">Symétrie non cristallographique</font> (''Fr''). <font color="black">Simmetria non cristallografica</font> (''It''). <font color="purple">非結晶的対称</font> (''Ja'').
 == Definition ==
-A symmetry operation that is not compatible with the periodicity of a [[crystal pattern]] (in two or three dimensions) is called a '''noncrystallographic symmetry'''. Rotations other than 1, 2, 3, 4, and 6 (in E<sup>2</sup> and E<sup>3</sup>) belong to this type of symmetry. Rotations 5, 8, 10 and 12 are compatible with a translation in higher-dimensional spaces, but they are commonly considered  noncrystallographic. For example, in quasicrystals fivefold or tenfold rotational axes are incapable of tiling space through the application of three-dimensional lattice translations, but they act as normal symmetry axes in a higher-dimensional space. Continuous rotations, which give rise to the Curie groups contained in the [[cylindrical system]] and in the [[spherical system]], are noncrystallographic in any dimension.
+A symmetry operation that is not compatible with the periodicity of a [[crystal pattern]] (in two or three dimensions) is called a '''noncrystallographic symmetry'''. Rotations other than 1, 2, 3, 4, and 6 (in ''E''<sup>2</sup> and ''E''<sup>3</sup>) belong to this type of symmetry. Rotations 5, 8, 10 and 12 are compatible with a translation in higher-dimensional spaces, but they are commonly considered  noncrystallographic. For example, in quasicrystals fivefold or tenfold rotational axes are incapable of tiling space through the application of three-dimensional lattice translations, but they act as normal symmetry axes in a higher-dimensional space. Continuous rotations, which give rise to the Curie groups contained in the [[cylindrical system]] and in the [[spherical system]], are noncrystallographic in any dimension.
 == Discussion ==
 In [[:Category:biological crystallography|biological crystallography]], the term  'noncrystallographic symmetry' is often, but improperly, used to indicate a symmetry relationship between similar subunits within the crystallographic asymmetric unit. This use comes from the fact that the operation required to superimpose one subunit on another is similar to a [[space group]] operation, but it operates only over a local volume, and the superposition may be inexact because the subunits are in different environments. The 'subunit' can be a molecular aggregate, a single molecule, a monomer unit of an oligomeric molecule, or a fragment of a molecule. The superposition is inexact because protein subunits in different environments are never identical. At the very least, surface side chains are differently ordered, and solvation is different because of different interactions with adjacent subunits.
 This use of the term 'noncrystallographic symmetry' is improper for two reasons:
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 ==See also==
-*Section 3.2.1.4 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 3.2.1.4 of ''International Tables for Crystallography, Volume A'', 6th edition
-*Section 2.3.5 of ''International Tables for Crystallography, Volume B''
+*Chapter 2.3.5 of ''International Tables for Crystallography, Volume B''
-*[http://www.degruyter.com/view/j/zkri.2008.223.issue-9/zkri.2008.1137/zkri.2008.1137.xml Discussion where the nomenclature issue is addressed]
+*[http://www.degruyter.com/view/j/zkri.2008.223.issue-9/zkri.2008.1137/zkri.2008.1137.xml Nespolo, M., Souvignier, B. and Litvin, D. B. (2008). ''Z. Kryst. – Crystalline Mater.'' '''223''', 605–606]. ''About the concept and definition of “noncrystallographic symmetry"''
 [[Category:Fundamental crystallography]]
 [[Category:Biological crystallography]]

@@ Line 14: / Line 14: @@
 ==See also==
-*Section 10.1.4 of ''International Tables for Crystallography, Volume A''
+*Section 3.2.1.4 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
 *Section 2.3.5 of ''International Tables for Crystallography, Volume B''
 *[http://www.degruyter.com/view/j/zkri.2008.223.issue-9/zkri.2008.1137/zkri.2008.1137.xml Discussion where the nomenclature issue is addressed]

← Older revision		Revision as of 22:31, 26 November 2016
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−	<font color="blue">Symétrie non cristallographique</font> (''Fr''); <font color="black">Simmetria non cristallografica</font> (''It''); <font color="purple">~~非結晶学的対対称~~</font> (''Ja'')	+	<font color="blue">Symétrie non cristallographique</font> (''Fr''); <font color="black">Simmetria non cristallografica</font> (''It''); <font color="purple">非結晶的対称</font> (''Ja'')

	== Definition ==		== Definition ==

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 == Definition ==
-A symmetry operation that is not compatible with the periodicity of a [[crystal pattern]] (in two or three dimensions) is called a '''noncrystallographic symmetry'''. Rotations other than 1, 2, 3, 4, and 6 (in E<sup>2</sup> and E<sup>3</sup>) belong to this type of symmetry. Rotations 5, 8, 10 and 12 are compatible with a translation in higher-dimensional spaces, but they are commonly considered  noncrystallographic. For example、in quasicrystals fivefold or tenfold rotational axes are incapable of tiling space through the application of three-dimensional lattice translations, but they act as normal symmetry axes in a higher-dimensional space. Continous rotations, which give rise to the Curie groups contained in the [[cylindrical system]] and in the [[spherical system]], are noncrystallographic in any dimension.
+A symmetry operation that is not compatible with the periodicity of a [[crystal pattern]] (in two or three dimensions) is called a '''noncrystallographic symmetry'''. Rotations other than 1, 2, 3, 4, and 6 (in E<sup>2</sup> and E<sup>3</sup>) belong to this type of symmetry. Rotations 5, 8, 10 and 12 are compatible with a translation in higher-dimensional spaces, but they are commonly considered  noncrystallographic. For example, in quasicrystals fivefold or tenfold rotational axes are incapable of tiling space through the application of three-dimensional lattice translations, but they act as normal symmetry axes in a higher-dimensional space. Continuous rotations, which give rise to the Curie groups contained in the [[cylindrical system]] and in the [[spherical system]], are noncrystallographic in any dimension.
 == Discussion ==

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 This use of the term 'noncrystallographic symmetry' is improper for two reasons:
-#a symmetry operation acting on a subspace of the crystal space is called a [[local symmetry]] operation; it is a space [[groupoid]] operation;
+#a symmetry operation acting on a subspace of the crystal space is called a [[local symmetry|local]] or [[partial symmetry]] operation; it is a space [[groupoid]] operation;
 #an operation that superposes two objects only approximately is called a [[pseudo symmetry]] operation.