Sohncke groups

From Online Dictionary of Crystallography

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

Sohncke groups are called 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.


  • C. Jordan (1869). Mémoire sur les groupes de mouvements. Annali di Matematica Pura ed Applicata (1867-1897), August 1868, Volume 2, Issue 1, pp 167-215
  • L. Sohncke (1879). Entwickelung einer Theorie der Krystallstruktur. B.G. Teubner, Leipzig