# Difference between revisions of "Fixed-point-free space group"

### From Online Dictionary of Crystallography

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*[[Point configuration]] | *[[Point configuration]] | ||

*[[Wyckoff position]] | *[[Wyckoff position]] | ||

− | * Chapter 1.4.4.2 of ''International Tables for Crystallography'', Volume A, 6th edition | + | * 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 *E*^{2}

Only two ﬁxed-point-free space groups exist in *E*^{2}: *p*1 and *pg*.

## Fixed-point-free space groups in *E*^{3}

Thirteen ﬁxed-point-free space groups exist in *E*^{3}: *P*1, *P*2_{1}, *Pc*, *Cc*, *P*2_{1}2_{1}2_{1}, *Pca*2_{1}, *Pna*2_{1}, *P*4_{1}, *P*4_{3}, *P*3_{1}, *P*3_{2}, *P*6_{1}, *P*6_{5}.

## See also

- Crystallographic orbit
- Point configuration
- Wyckoff position
- Chapter 1.4.4.2 of
*International Tables for Crystallography*,*Volume A*, 6th edition