Difference between revisions of "Fixed-point-free space group"
From Online Dictionary of Crystallography
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| − | [[Space group]]s with no special [[Wyckoff position]]s (''i''.''e''. with no special [[crystallographic orbit]]s) are called '''fixed-point-free space groups'''. | + | [[Space group]]s with no special [[Wyckoff position]]s (''i''.''e''. with no special [[crystallographic orbit]]s) 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 E<sup>2</sup>== | ==Fixed-point-free space groups in E<sup>2</sup>== | ||
Revision as of 19:55, 24 August 2014
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 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
- crystallographic orbit
- point configuration
- Wyckoff position
- Section 8.3.2 of the International Tables of Crystallography, Volume A