Hermann-Mauguin symbols - Revision history

BrianMcMahon: Tidied translations.

2017-12-01T16:56:50Z

Tidied translations.

BrianMcMahon: Tidied translations.

2017-11-14T09:41:56Z

Tidied translations.

BrianMcMahon: Style edits to align with printed edition

2017-05-19T16:09:32Z

Style edits to align with printed edition

BrianMcMahon: Style edits to align with printed edition

2017-05-15T14:03:30Z

Style edits to align with printed edition

MassimoNespolo: bold, assded "point group"

2016-11-30T12:58:27Z

bold, assded "point group"

MassimoNespolo: lang

2016-11-24T18:18:53Z

lang

MassimoNespolo: Created page with "Symboles d'Hermann-Mauguin　(''Fr''). Simboli di Hermann-Mauguin　(''It''). ヘルマン・モーガ..."

2016-11-24T13:42:08Z

Created page with "Symboles d'Hermann-Mauguin　(''Fr''). Simboli di Hermann-Mauguin　(''It''). ヘルマン・モーガ..."

New page

Symboles d'Hermann-Mauguin　(''Fr''). Simboli di Hermann-Mauguin　(''It''). ヘルマン・モーガン記号　(''Ja'')

'''Hermann-Mauguin''' symbols, also known as international symbols, are oriented symbols giving the [[symmetry operation]]s or [[symmetry element]]s of a [[space group]]. Three types of Hermann-Mauguin are used: ''short'', ''full'' and ''extended''. The three types of symbols represent different levels of information content with respect to the symmetry elements and the related symmetry operations of the space group.

The short and full Hermann-Mauguin symbols only display information about a chosen set of generators for a space group from which all elements of a space group can in principle be deduced. Both the short and the full Hermann-Mauguin symbols consist of two parts:
*a letter indicating the centring type of the conventional cell, and
*a set of characters indicating symmetry elements of the space group parallel or perpendicular to the symmetry directions of the lattice of the space group.
In general, the symbol of symmetry elements shown in the Hermann-Mauguin symbols are selected according to the so-called priority rule which requires that rotation axes are chosen over screw axes of the same rotational order, when these coexist along the same symmetry direction, and mirror planes are chosen in the sequence ''m'' > ''e'' > ''a'', ''b'', ''c'' > ''n'' (where > means “has priority over”). A few exceptions occur when these rules would not allow differentiating space-group types bringing the same type of symmetry elements but differently positioned in space, like ''I''222 (No. 23) and ''I''212121 (No. 24), where the rotation axes cross in a point for the former but not for the latter.

'''Short''' and '''full''' Hermann-Mauguin symbols coincide for most space groups with the exception of the monoclinic space groups (the full symbol explicitly states the symmetry direction: for example, ''Pc'' short symbol vs. ''P''1''c''1 full symbol), the space groups of the [[holohedry|holohedries]] (with the exception of ''P''-1) and of the geometric crystal class ''m''-3 (for example, ''Pa''-3 short symbol vs. ''P''21/''a''-3 full symbol). Short symbols give a reduced set of symmetry elements about the symmetry directions of the lattice, where reduced means that some of the symmetry elements along certain symmetry directions may not be explicitly shown.

In the orthorhombic or higher crystal systems when a symmetry axis of order two and a normal to a symmetry plane are parallel, in the full symbols, the symmetry axes and symmetry planes normal to them for each symmetry direction are listed while in the short symbols, only the symmetry-planes symbols are shown. For example, the full and short symbol of space-group type No. 55 are, respectively, ''P''21/''b''21/''a''2/''m'' and ''Pbam''. This reduced set of symmetry elements shown in the short Hermann-Mauguin symbols is however not limited to the elements corresponding to the generators of the space group; for example, in orthorhombic merohedral space groups the operations corresponding to the symmetry elements about two of the three symmetry directions of the lattice are generators, the third is obtained as the product (composition) of these two.

In the '''extended''' Hermann-Mauguin symbols, the symmetry of the space group is listed in a rather complete fashion and provide information not only on the chosen set of space-group generators but also on the additional symmetry operations in most of the cases obtained by the compositions of the generating symmetry operations with lattice translations. These symbols are constructed following the same rules as the short symbols but give the corresponding full list of symmetry operations, including the different symmetry operation of the same nature (rotation or screw rotations of the same order; mirror or glide reflections) that may occur about geometric elements in parallel orientation. The result is a symbol composed of one (when the extended symbols coincides with the short one), two or four lines depending on the crystal system and the type of unit cell.

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 16:56, 1 December 2017
Line 1:		Line 1:
−	<font color="blue">Symboles d'Hermann-Mauguin</font> (''Fr''). <font color="red">Hermann-Mauguin-Symbolik</font> (''Ge''). <font color="black">Simboli di Hermann-Mauguin</font> (''It''). <font color="~~brown~~">~~Символика Германа — Могена~~</font> (''Ru''). <font color="~~purple~~">~~ヘルマン・モーガン記号~~</font> (''Ja''). <font color="green">Símbolos de Hermann-Mauguin</font> (''Sp'').	+	<font color="blue">Symboles d'Hermann-Mauguin</font> (''Fr''). <font color="red">Hermann-Mauguin-Symbolik</font> (''Ge''). <font color="black">Simboli di Hermann-Mauguin</font> (''It''). <font color="purple">ヘルマン・モーガン記号</font> (''Ja''). <font color="brown">Символика Германа — Могена</font> (''Ru''). <font color="green">Símbolos de Hermann-Mauguin</font> (''Sp'').

← Older revision		Revision as of 09:41, 14 November 2017
Line 1:		Line 1:
−	<~~Font~~ color="blue">Symboles d'Hermann-Mauguin</~~Font~~> (''Fr''). <~~Font~~ color="red">Hermann-Mauguin-Symbolik</~~Font~~> (''Ge''). <~~Font~~ color="~~green~~">~~Símbolos de~~ Hermann-Mauguin</~~Font~~> (''Sp''). <~~Font~~ color="~~black~~">~~Simboli di Hermann-Mauguin~~</~~Font~~> (''It''). <~~Font~~ color="~~brown~~">~~Символика Германа — Могена~~</~~Font~~> (''Ru''). <~~Font~~ color="~~purple~~"> ~~ヘルマン・モーガン記号~~</~~Font~~>　(''Ja'').	+	<font color="blue">Symboles d'Hermann-Mauguin</font> (''Fr''). <font color="red">Hermann-Mauguin-Symbolik</font> (''Ge''). <font color="black">Simboli di Hermann-Mauguin</font> (''It''). <font color="brown">Символика Германа — Могена</font> (''Ru''). <font color="purple">ヘルマン・モーガン記号</font> (''Ja''). <font color="green">Símbolos de Hermann-Mauguin</font> (''Sp'').

@@ Line 2: / Line 2: @@
-'''Hermann-Mauguin''' symbols, also known as '''international symbols''', are oriented symbols giving the [[symmetry operation]]s or [[symmetry element]]s of a [[point group|point]] or [[space group]]. Three types of Hermann-Mauguin are used: ''short'', ''full'' and, for space groups, ''extended''. The three types of symbols represent different levels of information content with respect to the symmetry elements and the related symmetry operations of the space group.
+'''Hermann-Mauguin''' symbols, also known as '''international symbols''', are oriented symbols giving the [[symmetry operation]]s or [[symmetry element]]s of a [[point group|point]] or [[space group]]. Three types of Hermann-Mauguin symbol are used: ''short'', ''full'' and, for space groups, ''extended''. The three types of symbols represent different levels of information content with respect to the symmetry elements and the related symmetry operations of the space group.
 The short and full Hermann-Mauguin symbols only display information about a chosen set of generators for a space group from which all elements of a space group can in principle be deduced. Both the short and the full Hermann-Mauguin symbols consist of two parts:
 *a letter indicating the centring type of the conventional cell, and
 *a set of characters indicating symmetry elements of the space group parallel or perpendicular to the symmetry directions of the lattice of the space group.
-In general, the symbol of symmetry elements shown in the Hermann-Mauguin symbols are selected according to the so-called priority rule which requires that rotation axes are chosen over screw axes of the same rotational order, when these coexist along the same symmetry direction, and mirror planes are chosen in the sequence ''m'' > ''e'' > ''a'', ''b'', ''c'' > ''n'' (where > means 'has priority over'). A few exceptions occur when these rules would not allow differentiating space-group types bringing the same type of symmetry elements but differently positioned in space, like ''I''222 (No. 23) and ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> (No. 24), where the rotation axes cross in a point for the former but not for the latter.
+In general, the symbols for symmetry elements shown in the Hermann-Mauguin symbols are selected according to the so-called ''priority rule'' which requires that rotation axes are chosen over screw axes of the same rotational order, when these coexist along the same symmetry direction, and mirror planes are chosen in the sequence ''m'' > ''e'' > ''a'', ''b'', ''c'' > ''n'' (where > means 'has priority over'). A few exceptions occur when these rules would not allow differentiating space-group types bringing the same type of symmetry elements but differently positioned in space, like ''I''222 (No. 23) and ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> (No. 24), where the rotation axes cross in a point for the former but not for the latter.
-'''Short''' and '''full''' Hermann-Mauguin symbols coincide for most space groups with the exception of the monoclinic space groups (the full symbol explicitly states the symmetry direction: for example, ''Pc'' short symbol ''vs'' ''P''1''c''1 full symbol), the space groups of the [[holohedry|holohedries]] (with the exception of ''P''-1) and of the geometric crystal class ''m''-3 (for example, ''Pa''-3 short symbol ''vs'' ''P''2<sub>1</sub>/''a''-3 full symbol). Short symbols give a reduced set of symmetry elements about the symmetry directions of the lattice, where reduced means that some of the symmetry elements along certain symmetry directions may not be explicitly shown.
+'''Short''' and '''full''' Hermann-Mauguin symbols coincide for most space groups with the exception of the monoclinic space groups (the full symbol explicitly states the symmetry direction: for example, ''Pc'' short symbol ''vs'' ''P''1''c''1 full symbol), the space groups of the [[holohedry|holohedries]] (with the exception of ''P''-1) and of the geometric crystal class ''m''-3 (for example, ''Pa''-3 short symbol ''vs'' ''P''2<sub>1</sub>/''a''-3 full symbol). Short symbols give a reduced set of symmetry elements about the symmetry directions of the lattice, where 'reduced' means that some of the symmetry elements along certain symmetry directions may not be explicitly shown.
-In the orthorhombic or higher crystal systems when a symmetry axis of order two and a normal to a symmetry plane are parallel, in the full symbols, the symmetry axes and symmetry planes normal to them for each symmetry direction are listed while in the short symbols, only the symmetry-planes symbols are shown. For example, the full and short symbol of space-group type No. 55 are, respectively, ''P''2<sub>1</sub>/''b''2<sub>1</sub>/''a''2/''m'' and ''Pbam''. This reduced set of symmetry elements shown in the short Hermann-Mauguin symbols is however not limited to the elements corresponding to the generators of the space group; for example, in orthorhombic merohedral space groups the operations corresponding to the symmetry elements about two of the three symmetry directions of the lattice are generators, the third is obtained as the product (composition) of these two.
+In the orthorhombic or higher crystal systems, when a symmetry axis of order two and a normal to a symmetry plane are parallel, in the full symbols the symmetry axes and symmetry planes normal to them for each symmetry direction are listed, while in the short symbols only the symmetry-planes symbols are shown. For example, the full and short symbols of space-group type No. 55 are, respectively, ''P''2<sub>1</sub>/''b''2<sub>1</sub>/''a''2/''m'' and ''Pbam''. This reduced set of symmetry elements shown in the short Hermann-Mauguin symbols is however not limited to the elements corresponding to the generators of the space group; for example, in orthorhombic merohedral space groups the operations corresponding to the symmetry elements about two of the three symmetry directions of the lattice are generators, the third is obtained as the product (composition) of these two.
-In the '''extended''' Hermann-Mauguin symbols, the symmetry of the space group is listed in a rather complete fashion and provide information not only on the chosen set of space-group generators but also on the additional symmetry operations in most of the cases obtained by the compositions of the generating symmetry operations with lattice translations. These symbols are constructed following the same rules as the short symbols but give the corresponding full list of symmetry operations, including the different symmetry operation of the same nature (rotation or screw rotations of the same order; mirror or glide reflections) that may occur about geometric elements in parallel orientation. The result is a symbol composed of one (when the extended symbols coincides with the short one), two or four lines depending on the crystal system and the type of unit cell.
+In the '''extended''' Hermann-Mauguin symbols, the symmetry of the space group is listed in a rather complete fashion and provides information not only on the chosen set of space-group generators but also on the additional symmetry operations in most of the cases obtained by the compositions of the generating symmetry operations with lattice translations. These symbols are constructed following the same rules as the short symbols but give the corresponding full list of symmetry operations, including the different symmetry operations of the same nature (rotation or screw rotations of the same order; mirror or glide reflections) that may occur about geometric elements in parallel orientation. The result is a symbol composed of one (when the extended symbols coincides with the short one), two or four lines depending on the crystal system and the type of unit cell.
 [[Category:Fundamental crystallography]]

@@ Line 1: / Line 1: @@
-<Font color="blue">Symboles d'Hermann-Mauguin</Font>　(''Fr''); <Font color="red">Hermann-Mauguin-Symbolik</Font>　(''Ge''); <Font color="green">Símbolos de Hermann-Mauguin</Font>　(''Sp'');  <Font color="black">Simboli di Hermann-Mauguin</Font>　(''It'');. <Font color="brown">Символика Германа — Могена</Font>　(''Ru''); <Font color="purple"> ヘルマン・モーガン記号</Font>　(''Ja'').
+<Font color="blue">Symboles d'Hermann-Mauguin</Font> (''Fr''). <Font color="red">Hermann-Mauguin-Symbolik</Font> (''Ge''). <Font color="green">Símbolos de Hermann-Mauguin</Font> (''Sp'').  <Font color="black">Simboli di Hermann-Mauguin</Font> (''It''). <Font color="brown">Символика Германа — Могена</Font> (''Ru''). <Font color="purple"> ヘルマン・モーガン記号</Font>　(''Ja'').
@@ Line 7: / Line 7: @@
 *a letter indicating the centring type of the conventional cell, and
 *a set of characters indicating symmetry elements of the space group parallel or perpendicular to the symmetry directions of the lattice of the space group.
-In general, the symbol of symmetry elements shown in the Hermann-Mauguin symbols are selected according to the so-called priority rule which requires that rotation axes are chosen over screw axes of the same rotational order, when these coexist along the same symmetry direction, and mirror planes are chosen in the sequence ''m'' > ''e'' > ''a'', ''b'', ''c'' > ''n'' (where > means “has priority over”). A few exceptions occur when these rules would not allow differentiating space-group types bringing the same type of symmetry elements but differently positioned in space, like ''I''222 (No. 23) and ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> (No. 24), where the rotation axes cross in a point for the former but not for the latter.
+In general, the symbol of symmetry elements shown in the Hermann-Mauguin symbols are selected according to the so-called priority rule which requires that rotation axes are chosen over screw axes of the same rotational order, when these coexist along the same symmetry direction, and mirror planes are chosen in the sequence ''m'' > ''e'' > ''a'', ''b'', ''c'' > ''n'' (where > means 'has priority over'). A few exceptions occur when these rules would not allow differentiating space-group types bringing the same type of symmetry elements but differently positioned in space, like ''I''222 (No. 23) and ''I''2<sub>1</sub>2<sub>1</sub>2<sub>1</sub> (No. 24), where the rotation axes cross in a point for the former but not for the latter.
-'''Short''' and '''full''' Hermann-Mauguin symbols coincide for most space groups with the exception of the monoclinic space groups (the full symbol explicitly states the symmetry direction: for example, ''Pc'' short symbol vs. ''P''1''c''1 full symbol), the space groups of the [[holohedry|holohedries]] (with the exception of ''P''-1) and of the geometric crystal class ''m''-3 (for example, ''Pa''-3 short symbol vs. ''P''2<sub>1</sub>/''a''-3 full symbol). Short symbols give a reduced set of symmetry elements about the symmetry directions of the lattice, where reduced means that some of the symmetry elements along certain symmetry directions may not be explicitly shown.
+'''Short''' and '''full''' Hermann-Mauguin symbols coincide for most space groups with the exception of the monoclinic space groups (the full symbol explicitly states the symmetry direction: for example, ''Pc'' short symbol ''vs'' ''P''1''c''1 full symbol), the space groups of the [[holohedry|holohedries]] (with the exception of ''P''-1) and of the geometric crystal class ''m''-3 (for example, ''Pa''-3 short symbol ''vs'' ''P''2<sub>1</sub>/''a''-3 full symbol). Short symbols give a reduced set of symmetry elements about the symmetry directions of the lattice, where reduced means that some of the symmetry elements along certain symmetry directions may not be explicitly shown.
 In the orthorhombic or higher crystal systems when a symmetry axis of order two and a normal to a symmetry plane are parallel, in the full symbols, the symmetry axes and symmetry planes normal to them for each symmetry direction are listed while in the short symbols, only the symmetry-planes symbols are shown. For example, the full and short symbol of space-group type No. 55 are, respectively, ''P''2<sub>1</sub>/''b''2<sub>1</sub>/''a''2/''m'' and ''Pbam''. This reduced set of symmetry elements shown in the short Hermann-Mauguin symbols is however not limited to the elements corresponding to the generators of the space group; for example, in orthorhombic merohedral space groups the operations corresponding to the symmetry elements about two of the three symmetry directions of the lattice are generators, the third is obtained as the product (composition) of these two.

← Older revision		Revision as of 12:58, 30 November 2016
Line 2:		Line 2:


−	'''Hermann-Mauguin''' symbols, also known as international symbols, are oriented symbols giving the [[symmetry operation]]s or [[symmetry element]]s of a [[space group]]. Three types of Hermann-Mauguin are used: ''short'', ''full'' and ''extended''. The three types of symbols represent different levels of information content with respect to the symmetry elements and the related symmetry operations of the space group.	+	'''Hermann-Mauguin''' symbols, also known as '''international symbols''', are oriented symbols giving the [[symmetry operation]]s or [[symmetry element]]s of a [[point group\|point]] or [[space group]]. Three types of Hermann-Mauguin are used: ''short'', ''full'' and, for space groups, ''extended''. The three types of symbols represent different levels of information content with respect to the symmetry elements and the related symmetry operations of the space group.

	The short and full Hermann-Mauguin symbols only display information about a chosen set of generators for a space group from which all elements of a space group can in principle be deduced. Both the short and the full Hermann-Mauguin symbols consist of two parts:		The short and full Hermann-Mauguin symbols only display information about a chosen set of generators for a space group from which all elements of a space group can in principle be deduced. Both the short and the full Hermann-Mauguin symbols consist of two parts:

← Older revision		Revision as of 18:18, 24 November 2016
Line 1:		Line 1:
−	<Font color="blue">Symboles d'Hermann-Mauguin</Font>　(''Fr''). <Font color="black">Simboli di Hermann-Mauguin</Font>　(''It''). <Font color="purple"> ヘルマン・モーガン記号</Font>　(''Ja'')	+	<Font color="blue">Symboles d'Hermann-Mauguin</Font>　(''Fr''); <Font color="red">Hermann-Mauguin-Symbolik</Font>　(''Ge''); <Font color="green">Símbolos de Hermann-Mauguin</Font>　(''Sp''); <Font color="black">Simboli di Hermann-Mauguin</Font>　(''It'');. <Font color="brown">Символика Германа — Могена</Font>　(''Ru''); <Font color="purple"> ヘルマン・モーガン記号</Font>　(''Ja'').

Hermann-Mauguin symbols - Revision history

BrianMcMahon: Tidied translations.

BrianMcMahon: Tidied translations.

BrianMcMahon: Style edits to align with printed edition

BrianMcMahon: Style edits to align with printed edition

MassimoNespolo: bold, assded "point group"

MassimoNespolo: lang

MassimoNespolo: Created page with "Symboles d'Hermann-Mauguin (''Fr''). Simboli di Hermann-Mauguin (''It''). ヘルマン・モーガ..."

MassimoNespolo: Created page with "Symboles d'Hermann-Mauguin　(''Fr''). Simboli di Hermann-Mauguin　(''It''). ヘルマン・モーガ..."