Geometric element - Revision history

MassimoNespolo: Text moved to symmetry element, where it actually belongs.

2018-11-30T15:06:10Z

Text moved to symmetry element, where it actually belongs.

BrianMcMahon: Tidied translations and added German and Spanish (U. Mueller)

2017-11-13T14:39:53Z

Tidied translations and added German and Spanish (U. Mueller)

BrianMcMahon at 12:58, 7 July 2017

2017-07-07T12:58:36Z

BrianMcMahon: Style edits to align with printed edition

2017-05-12T10:02:35Z

Style edits to align with printed edition

MassimoNespolo: /* See also */

2017-04-10T15:44:56Z

‎See also

MassimoNespolo: slighlty revised Japanese translation

2017-01-05T12:27:16Z

slighlty revised Japanese translation

MassimoNespolo: more precise defintion for rotoinversions

2014-06-05T17:07:59Z

more precise defintion for rotoinversions

MassimoNespolo: Page created to differentiate between geometric element and symmetry element

2014-06-05T12:19:19Z

Page created to differentiate between geometric element and symmetry element

New page

Élément géométrique (''Fr''); Elemento geometrico (''It''); 幾何学要素 (''Ja'').

A '''geometric element''' is a [[direct lattice|lattice]] element about which a [[symmetry operation]] is performed. Geometric 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 geometric element that exists in this space is the '''reflection point''' (mirror point).

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

==See also==
[[Symmetry element]]

==References==
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.

[[Category:Fundamental crystallography]]

@@ Line 1: / Line 1: @@
 <font color="blue">Élément géométrique</font> (''Fr''). <font color="red">Geometrische Element</font> (''Ge''). <font color="black">Elemento geometrico</font> (''It''). <font color="purple">幾何的要素</font> (''Ja''). <font color="green">Elemento geométrico</font> (''Sp'').
 A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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==
+In one-dimensional spaces ''N''-1 = 0 and the only geometric element is a point. In two-dimensional spaces ''N''-1 = 1 and we have points and lines. In three-dimensional spaces ''N''-1 = 2 and we have points, lines and planes. In four-dimensional spaces ''N''-1 = 3 and we have points, lines, planes and hyperplanes.
 ==See also==

← Older revision		Revision as of 14:39, 13 November 2017
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−	<font color="blue">Élément géométrique</font> (''Fr''); <font color="black">Elemento geometrico</font> (''It''); <font color="purple">幾何的要素</font> (''Ja'').	+	<font color="blue">Élément géométrique</font> (''Fr''). <font color="red">Geometrische Element</font> (''Ge''). <font color="black">Elemento geometrico</font> (''It''). <font color="purple">幾何的要素</font> (''Ja''). <font color="green">Elemento geométrico</font> (''Sp'').

	A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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.		A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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.

@@ Line 21: / Line 21: @@
 ==See also==
 *[[Symmetry element]]
-*Section 1.2.3 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
+*Section 1.2.3 of ''International Tables for Crystallography, Volume A'', 6th edition
 ==Reference==

← Older revision		Revision as of 12:27, 5 January 2017
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−	<font color="blue">Élément géométrique</font> (''Fr''); <font color="black">Elemento geometrico</font> (''It''); <font color="purple">~~幾何学要素~~</font> (''Ja'').	+	<font color="blue">Élément géométrique</font> (''Fr''); <font color="black">Elemento geometrico</font> (''It''); <font color="purple">幾何的要素</font> (''Ja'').

	A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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.		A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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.

@@ Line 1: / Line 1: @@
 <font color="blue">Élément géométrique</font> (''Fr''); <font color="black">Elemento geometrico</font> (''It''); <font color="purple">幾何的要素</font> (''Ja'').
-A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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.
+A '''geometric element''' is an element in space (plane, line, point, or a combination of these) about which a [[symmetry operation]] is performed. Geometric 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==
@@ Line 8: / Line 8: @@
 ==Two-dimensional space==
 In this space, two types of geometric elements exist: zero and one-dimensional:
-*'''rotations points'''
+*'''rotation points'''
 *'''reflection lines''' (mirror lines)
 The inversion centre (point) does not exist in spaces of even number of dimensions.
@@ Line 15: / Line 15: @@
 In this space, three types of geometric elements exist: zero, one- and two-dimensional:
 *'''inversion centres'''
-*'''rotations axes'''
+*'''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.
@@ Line 23: / Line 23: @@
 *Section 1.2.3 of ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
-==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]]