Point group - Revision history

MassimoNespolo at 15:48, 30 November 2018

2018-11-30T15:48:27Z

MassimoNespolo: /* Controversy on the nomenclature */ element -> operation

2018-01-22T16:08:54Z

‎Controversy on the nomenclature: element -> operation

BrianMcMahon: Tidied translations.

2017-11-17T09:52:56Z

Tidied translations.

MassimoNespolo: /* Controversy on the nomenclature */ typo

2017-10-12T09:30:00Z

‎Controversy on the nomenclature: typo

MassimoNespolo: lang

2017-10-12T09:26:00Z

lang

BrianMcMahon at 13:02, 16 May 2017

2017-05-16T13:02:15Z

BrianMcMahon: Style edits to align with printed edition

2017-05-16T13:01:58Z

Style edits to align with printed edition

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

2017-04-10T16:25:06Z

‎See also: 6th edition of ITA

MassimoNespolo: lang

2016-11-30T13:00:58Z

lang

MassimoNespolo: Controversy on the nomenclature

2015-03-20T04:23:48Z

Controversy on the nomenclature

@@ Line 2: / Line 2: @@
 ==Definition==
-A '''point group''' is a group of symmetry operations all of which leave at least one point unmoved. A ''crystallographic'' point group is a point group that maps a point lattice onto itself: in three dimensions rotations and rotoinversions are restricted to 1, 2, 3, 4, 6 and <math>\bar 1</math>, <math>\bar 2</math> (= ''m''), <math>\bar 3</math>, <math>\bar 4</math>, <math>\bar 6</math> respectively.
+A '''point group''' is a group of symmetry operations all of which leave at least one point unmoved. A ''crystallographic'' point group is a point group that maps a point lattice onto itself: in three dimensions the symmetry operations of these groups are restricted to 1, 2, 3, 4, 6 and <math>\bar 1</math>, <math>\bar 2</math> (= ''m''), <math>\bar 3</math>, <math>\bar 4</math>, <math>\bar 6</math> respectively.
 ==Occurrence==

@@ Line 10: / Line 10: @@
 ==Controversy on the nomenclature==
-The matrix representation of a [[symmetry operation]] consists of a linear part, which represents the rotation or rotoinversion component of the operation, and a vector part, which gives the shift to be added once the linear part of the operation has been applied. The vector part is divided into two components: the ''intrinsic component'', which represents the screw and glide component of the operation, and the ''location component'', which is non-zero when the [[symmetry element]] does not pass through the origin. The set of the linear parts of the matrices representing the symmetry operations of a space group is a representation of the point group of the crystal. On the other hand, the set of matrix-vector pairs representing the symmetry operations of a [[site symmetry]] group form a group which is [[group isomorphism|isomorphic]] to a crystallographic point group. The vector part being in general non-zero, some authors reject the term ''point group'' for the [[site symmetry|site-symmetry groups]]. On the other hand, all the symmetry elements of a [[site symmetry]] group do leave invariant at least one point, albeit not necessarily the origin, satisfying the above definition of point group.
+The matrix representation of a [[symmetry operation]] consists of a linear part, which represents the rotation or rotoinversion component of the operation, and a vector part, which gives the shift to be added once the linear part of the operation has been applied. The vector part is divided into two components: the ''intrinsic component'', which represents the screw and glide component of the operation, and the ''location component'', which is non-zero when the [[symmetry element]] does not pass through the origin. The set of the linear parts of the matrices representing the symmetry operations of a space group is a representation of the point group of the crystal. On the other hand, the set of matrix-vector pairs representing the symmetry operations of a [[site symmetry]] group form a group which is [[group isomorphism|isomorphic]] to a crystallographic point group. The vector part being in general non-zero, some authors reject the term ''point group'' for the [[site symmetry|site-symmetry groups]]. On the other hand, all the [[symmetry operation]]s of a [[site symmetry]] group do leave invariant at least one point, albeit not necessarily the origin, satisfying the above definition of point group.
 ==See also==

← Older revision		Revision as of 09:52, 17 November 2017
Line 1:		Line 1:
−	<font color="orange">زمرة نقطية</font> (''Ar''); <font color="blue">Groupe ponctuel</font> (''Fr''); <font color="red">Punktgruppe</font> (''Ge''); <font color="black">Gruppo punto</font> (''It''); <font color="purple">点群</font> (''Ja''); <font color="brown">Точечная группа симметрии</font> (''Ru''); <font color="green">Grupo puntual</font> (''Sp'').	+	<font color="orange">زمرة نقطية</font> (''Ar''). <font color="blue">Groupe ponctuel</font> (''Fr''). <font color="red">Punktgruppe</font> (''Ge''). <font color="black">Gruppo punto</font> (''It''). <font color="purple">点群</font> (''Ja''). <font color="brown">Точечная группа симметрии</font> (''Ru''). <font color="green">Grupo puntual</font> (''Sp'').

	==Definition==		==Definition==

@@ Line 10: / Line 10: @@
 ==Controversy on the nomenclature==
-The matrix representation of a [[symmetry operation]] consists of a linear part, which represents the rotation or rotoinversion component of the operation, and a vector part, which gives the shift to be added once the linear part of the operation has been applied. The vector part is divided into two components: the ''intrinsic component'', which represents the screw and glide component of the operation, and the ''localization component'', which is non-zero when the [[symmetry element]] does not pass through the origin. The set of the linear parts of the matrices representing the symmetry operations of a space group is a representation of the point group of the crystal. On the other hand, the set of matrix-vector pairs representing the symmetry operations of a [[site symmetry]] group form a group which is [[group isomorphism|isomorphic]] to a crystallographic point group. The vector part being in general non-zero, some authors reject the term ''point group'' for the [[site symmetry|site-symmetry groups]]. On the other hand, all the symmetry elements of a [[site symmetry]] group do leave invariant at least one point, albeit not necessarily the origin, satisfying the above definition of point group.
+The matrix representation of a [[symmetry operation]] consists of a linear part, which represents the rotation or rotoinversion component of the operation, and a vector part, which gives the shift to be added once the linear part of the operation has been applied. The vector part is divided into two components: the ''intrinsic component'', which represents the screw and glide component of the operation, and the ''location component'', which is non-zero when the [[symmetry element]] does not pass through the origin. The set of the linear parts of the matrices representing the symmetry operations of a space group is a representation of the point group of the crystal. On the other hand, the set of matrix-vector pairs representing the symmetry operations of a [[site symmetry]] group form a group which is [[group isomorphism|isomorphic]] to a crystallographic point group. The vector part being in general non-zero, some authors reject the term ''point group'' for the [[site symmetry|site-symmetry groups]]. On the other hand, all the symmetry elements of a [[site symmetry]] group do leave invariant at least one point, albeit not necessarily the origin, satisfying the above definition of point group.
 ==See also==

← Older revision		Revision as of 09:26, 12 October 2017
Line 1:		Line 1:
−	<font color="blue">Groupe ponctuel</font> (''Fr''). <font color="red">Punktgruppe</font> (''Ge''). <font color="~~green~~">~~Grupo puntual~~</font> (''Sp''). <font color="~~black~~">~~Gruppo punto~~</font> (''It''). <font color="brown">Точечная группа симметрии</font> (''Ru''). <font color="~~purple~~">点群</font> (''Ja'').	+	<font color="orange">زمرة نقطية</font> (''Ar''); <font color="blue">Groupe ponctuel</font> (''Fr''); <font color="red">Punktgruppe</font> (''Ge''); <font color="black">Gruppo punto</font> (''It''); <font color="purple">点群</font> (''Ja''); <font color="brown">Точечная группа симметрии</font> (''Ru''); <font color="green">Grupo puntual</font> (''Sp'').

	==Definition==		==Definition==

@@ Line 7: / Line 7: @@
 Crystallographic point groups occur:
 * in [[vector space]], as symmetries of the external shapes of crystals (morphological symmetry), as well as symmetry of the physical properties of the crystal ('vector point group');
-* in [[point space]], as [[site symmetry|site-symmetry groups]] of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra ('point point group').
+* in [[point space]], as [[site symmetry|site-symmetry groups]] of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyhedra ('point point group').
 ==Controversy on the nomenclature==

@@ Line 1: / Line 1: @@
-<font color="blue">Groupe ponctuel</font> (''Fr''); <font color="red">Punktgruppe</font> (''Ge''); <font color="green">Grupo puntual</font> (''Sp''); <font color="black">Gruppo punto</font> (''It''); <font color="brown">Точечная группа симметрии</font> (''Ru''); <font color="purple">点群</font> (''Ja'').
+<font color="blue">Groupe ponctuel</font> (''Fr''). <font color="red">Punktgruppe</font> (''Ge''). <font color="green">Grupo puntual</font> (''Sp''). <font color="black">Gruppo punto</font> (''It''). <font color="brown">Точечная группа симметрии</font> (''Ru''). <font color="purple">点群</font> (''Ja'').
 ==Definition==
@@ Line 6: / Line 6: @@
 ==Occurrence==
 Crystallographic point groups occur:
-* in [[vector space]], as symmetries of the external shapes of crystals (morphological symmetry), as well as symmetry of the physical properties of the crystal ("vector point group");
+* in [[vector space]], as symmetries of the external shapes of crystals (morphological symmetry), as well as symmetry of the physical properties of the crystal ('vector point group');
-* in [[point space]], as [[site symmetry|site-symmetry groups]] of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra ("point point group").
+* in [[point space]], as [[site symmetry|site-symmetry groups]] of points in lattices or in crystal structures, and as symmetries of atomic groups and coordination polyedra ('point point group').
 ==Controversy on the nomenclature==
-The matrix representation of a [[symmetry operation]] consists of a linear part, which represents the rotation or rotoinversion component of the operation, and a vector part, which gives the shift to be added once the linear part of the operation has been applied. The vector part is divided into two components: the ''intrinsic component'', which represents the screw and glide component of the operation, and the ''localisation component'', which is non-zero when the [[symmetry element]] does not pass through the origin. The set of the linear parts of the matrices representing the symmetry operations of a space group is a representation of the point group of the crystal. On the other hand, the set of matrix-vector pairs representing the symmetry operations of a [[site symmetry]] group form a group which is [[group isomorphism|isomorphic]] to a crystallographic point group. The vector part being in general non-zero, some authors refuse the term ''point group'' for the [[site symmetry|site-symmetry groups]]. On the other hand, all the symmetry elements of a [[site symmetry]] group do leave invariant at least one point, albeit not necessarily the origin, satisfying the above definition of point group.
+The matrix representation of a [[symmetry operation]] consists of a linear part, which represents the rotation or rotoinversion component of the operation, and a vector part, which gives the shift to be added once the linear part of the operation has been applied. The vector part is divided into two components: the ''intrinsic component'', which represents the screw and glide component of the operation, and the ''localization component'', which is non-zero when the [[symmetry element]] does not pass through the origin. The set of the linear parts of the matrices representing the symmetry operations of a space group is a representation of the point group of the crystal. On the other hand, the set of matrix-vector pairs representing the symmetry operations of a [[site symmetry]] group form a group which is [[group isomorphism|isomorphic]] to a crystallographic point group. The vector part being in general non-zero, some authors reject the term ''point group'' for the [[site symmetry|site-symmetry groups]]. On the other hand, all the symmetry elements of a [[site symmetry]] group do leave invariant at least one point, albeit not necessarily the origin, satisfying the above definition of point group.
 ==See also==
-*Section 3.2.1 in ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 3.2.1 of ''International Tables for Crystallography, Volume A'', 6th edition
 [[Category:Fundamental crystallography]]

← Older revision		Revision as of 13:00, 30 November 2016
Line 1:		Line 1:
−	<font color="blue">Groupe ponctuel</font> (''Fr''); <font color="red">Punktgruppe</font> (''Ge''); <font color="black">Gruppo punto</font> (''It''); <font color="purple">点群</font> (''Ja'').	+	<font color="blue">Groupe ponctuel</font> (''Fr''); <font color="red">Punktgruppe</font> (''Ge''); <font color="green">Grupo puntual</font> (''Sp''); <font color="black">Gruppo punto</font> (''It''); <font color="brown">Точечная группа симметрии</font> (''Ru''); <font color="purple">点群</font> (''Ja'').

	==Definition==		==Definition==