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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* Section 8.3.2 of the ''International Tables of Crystallography'', Volume A
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* Section 1.4.4.2 of the ''International Tables of Crystallography'', Volume A, 6<sup>th</sup> edition
[[Category:Fundamental crystallography]]
[[Category:Fundamental crystallography]]

Revision as of 15:03, 10 April 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