Fixed-point-free space group
From Online Dictionary of Crystallography
Revision as of 11:02, 15 May 2017 by BrianMcMahon (Style edits to align with printed edition)
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.