Chiral space group

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.

• 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.

See also

• Chapter 3.5.1.2 of International Tables for Crystallography, Volume A, 6th edition