Fixed-point-free space group

From Online Dictionary of Crystallography

Revision as of 13:33, 13 November 2017 by BrianMcMahon (Talk | contribs)
Jump to: navigation, search

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.

See also