Fixed-point-free space group

From Online Dictionary of Crystallography

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*[[Point configuration]]
*[[Point configuration]]
*[[Wyckoff position]]
*[[Wyckoff position]]
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* Chapter 1.4.4.2 of  ''International Tables for Crystallography'', Volume A, 6th edition
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* Chapter 1.4.4.2 of  ''International Tables for Crystallography'', ''Volume A'', 6th edition
[[Category:Fundamental crystallography]]
[[Category:Fundamental crystallography]]

Revision as of 11:03, 15 May 2017

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