Fixed-point-free space group
From Online Dictionary of Crystallography
Revision as of 13:33, 13 November 2017 by BrianMcMahon (Added German and Spanish translations (U. Mueller))
Fixpunktfreie Raumgruppe, Bieberbachgruppe (Ge). Grupo espacial sin puntos fijos (Sp).
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 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 E2: p1 and pg.
Fixed-point-free space groups in E3
Thirteen ﬁxed-point-free space groups exist in E3: P1, P21, Pc, Cc, P212121, Pca21, Pna21, P41, P43, P31, P32, P61, P65.