Chiral space group

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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.

See also

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