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Fixed-point-free space groups

Space groups with  no  special  Wyckoff positions (i.e. with no special crystallographic orbits) are called fixed-point-free space groups or torsion-free space groups or Bieberbach groups. In fixed-point-free space groups group every element other than the identity has infinite order.

Fixed-point-free space groups in E2

Only two fixed-point-free space groups exist in E2p1 and pg.

Fixed-point-free space groups in E3

Thirteen fixed-point-free space groups exist in E3P1, P21PcCcP212121Pca21Pna21P41P43P31P32,P61P65.

See also

  •  Section 8.3.2 of the International Tables of Crystallography, Volume A