Difference between revisions of "Chiral space group"

Latest revision as of 17:09, 9 November 2017

Synonym: enantiomorphic space group

Groupe d'espace chiral (Fr). Chirale (oder enantiomorphe) Raumgruppe (Ge). Gruppo spaziale chirale (It). キラル空間群 (Ja). Grupo espacial quiral (o enantiomórfico) (Sp).

A chiral space group is a space group whose group structure is chiral: its Euclidean normalizer contains only operations of the first kind. Every chiral type of space group occurs in two enantiomorphic variants. In E³ there are thus 22 types of chiral space groups, forming 11 enantiomorphic pairs.

Classification scheme of space groups in three-dimensional space in terms of chirality.

P4₁-P4₃
P4₁22-P4₃22
P4₁2₁2-P4₃2₁2
P3₁-P3₂
P3₁21-P3₂21
P3₁12-P3₂12
P6₁-P6₅
P6₁22-P6₅22
P6₂-P6₄
P6₂22-P6₄22
P4₁32-P4₃32

A chiral crystal structure can occur not only in the 22 chiral space-group types but in any of the 65 Sohncke groups.

@@ Line 1: / Line 1: @@
-<font color="blue">Groupe d'espace chiral </font> (''Fr''), <font color="black">Gruppo spaziale chirale</font> (''It''). <font color="purple">キラル空間群</font> (''It'').
+Synonym: enantiomorphic space group
-A '''chiral space group''' is a space group whose group structure is [[chirality|chiral]]: its Euclidean [[normalizer]] contains only operations of the first kind. Every chiral type of [[space group]] occurs in two enantiomorphic variants. In E<sup>3</sup> there are thus 22 types of chiral space groups, forming 11 enantiomorphic pairs.
+<font color="blue">Groupe d'espace chiral</font> (''Fr''). <font color="red">Chirale (oder enantiomorphe) Raumgruppe</font> (''Ge''). <font color="black">Gruppo spaziale chirale</font> (''It''). <font color="purple">キラル空間群</font> (''Ja''). <font color="green">Grupo espacial quiral (o enantiomórfico)</font> (''Sp'').
-*P4<sub>1</sub>-P4<sub>3</sub>
+A '''chiral space group''' is a space group whose group structure is [[chirality|chiral]]: its Euclidean [[normalizer]] contains only operations of the first kind. Every chiral type of [[space group]] occurs in two enantiomorphic variants. In ''E''<sup>3</sup> there are thus 22 types of chiral space groups, forming 11 enantiomorphic pairs.
-*P4<sub>1</sub>22-P4<sub>3</sub>22
-*P4<sub>1</sub>2<sub>1</sub>2-P4<sub>3</sub>2<sub>1</sub>2
+[[Image:Sohncke-vs-chiral-scheme.png|500px|Classification scheme of space groups in three-dimensional space in terms of chirality.|right]]
-*P3<sub>1</sub>-P3<sub>2</sub>
-*P3<sub>1</sub>21-P3<sub>2</sub>21
+*''P''4<sub>1</sub>-''P''4<sub>3</sub>
-*P3<sub>1</sub>12-P3<sub>2</sub>12
+*''P''4<sub>1</sub>22-''P''4<sub>3</sub>22
-*P6<sub>1</sub>-P6<sub>5</sub>
+*''P''4<sub>1</sub>2<sub>1</sub>2-''P''4<sub>3</sub>2<sub>1</sub>2
-*P6<sub>1</sub>22-P6<sub>5</sub>22
+*''P''3<sub>1</sub>-''P''3<sub>2</sub>
-*P6<sub>2</sub>-P6<sub>4</sub>
+*''P''3<sub>1</sub>21-''P''3<sub>2</sub>21
-*P6<sub>2</sub>22-P6<sub>4</sub>22
+*''P''3<sub>1</sub>12-''P''3<sub>2</sub>12
-*P4<sub>1</sub>32-P4<sub>3</sub>32
+*''P''6<sub>1</sub>-''P''6<sub>5</sub>
+*''P''6<sub>1</sub>22-''P''6<sub>5</sub>22
+*''P''6<sub>2</sub>-''P''6<sub>4</sub>
+*''P''6<sub>2</sub>22-''P''6<sub>4</sub>22
+*''P''4<sub>1</sub>32-''P''4<sub>3</sub>32
 A chiral [[crystal pattern|crystal structure]] can occur not only in the 22 chiral space-group types but in any of the 65 [[Sohncke groups]].
+== See also ==
+*Chapter 3.5.1.2 of ''International Tables for Crystallography, Volume A'', 6th edition
 [[Category:Fundamental crystallography]]
 [[Category:Crystal chemistry]]

Difference between revisions of "Chiral space group"

From Online Dictionary of Crystallography

Latest revision as of 17:09, 9 November 2017

See also