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'''.  
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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''' 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