Sohncke groups

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Groupes de Sohncke (Fr). Sohncke-Raumgruppe (Ge). Grupos de Sohncke (Sp). Gruppi di Sohncke (It). ソンケ群 (Ja).

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

Sohncke groups are the 65 three-dimensional space groups containing only operations of the first kind (rotations, rototranslations, translations). Chiral crystal structures, including proteins, occur in these groups, not only in the chiral space groups.

The term comes from Leonhard Sohncke (Halle, 22 February 1842 – München, 1 November 1897), German mathematician, whose derivation was based on the results previously published by Marie Ennemond Camille Jordan (Lyon, 5 January 1838 – Paris, 22 January 1922), French mathematician.


  • Jordan, C. (1869). Annali di Matematica Pura ed Applicata (1867-1897), 2, 167-215. Mémoire sur les groupes de mouvements.
  • Sohncke, L. (1879). Entwickelung einer Theorie der Krystallstruktur. B. G. Teubner, Leipzig