# Difference between revisions of "Chiral space group"

### From Online Dictionary of Crystallography

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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. | 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. | ||

− | [[Image:Sohncke-vs-chiral-scheme.png|500px|Classification scheme of space groups in terms of chirality.|right]] | + | [[Image:Sohncke-vs-chiral-scheme.png|500px|Classification scheme of space groups in three-dimensional space in terms of chirality.|right]] |

*''P''4<sub>1</sub>-''P''4<sub>3</sub> | *''P''4<sub>1</sub>-''P''4<sub>3</sub> |

## Revision as of 08:02, 8 June 2017

Groupe d'espace chiral (*Fr*). Gruppo spaziale chirale (*It*). キラル空間群 (*Ja*).

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 *E*^{3} there are thus 22 types of chiral space groups, forming 11 enantiomorphic pairs.

*P*4_{1}-*P*4_{3}*P*4_{1}22-*P*4_{3}22*P*4_{1}2_{1}2-*P*4_{3}2_{1}2*P*3_{1}-*P*3_{2}*P*3_{1}21-*P*3_{2}21*P*3_{1}12-*P*3_{2}12*P*6_{1}-*P*6_{5}*P*6_{1}22-*P*6_{5}22*P*6_{2}-*P*6_{4}*P*6_{2}22-*P*6_{4}22*P*4_{1}32-*P*4_{3}32

A chiral 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