# Space group

### From Online Dictionary of Crystallography

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- | <font color="blue">Groupe d'espace</font> (''Fr''); <font color="red">Raumgruppe</font> (''Ge''); <font color="black">Gruppo spaziale</font> (''It''); <font color="purple">空間群</font> (''Ja''); <font color=" | + | <font color="orange">صنف أو مجموعة الفضاء</font> (''Ar''); <font color="blue">Groupe d'espace</font> (''Fr''); <font color="red">Raumgruppe</font> (''Ge''); <font color="black">Gruppo spaziale</font> (''It''); <font color="purple">空間群</font> (''Ja''); <font color="brown">Кристаллографическая группа</font> (''Ru''); <font color="green">Grupo espacial</font> (''Sp''). |

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The symmetry group of a three-dimensional [[crystal pattern]] is called its '''space group'''. In ''E''<sup>2</sup>, the symmetry group of a two-dimensional crystal pattern is called its '''plane group'''. In ''E''<sup>1</sup>, the symmetry group of a one-dimensional crystal pattern is called its '''line group'''. | The symmetry group of a three-dimensional [[crystal pattern]] is called its '''space group'''. In ''E''<sup>2</sup>, the symmetry group of a two-dimensional crystal pattern is called its '''plane group'''. In ''E''<sup>1</sup>, the symmetry group of a one-dimensional crystal pattern is called its '''line group'''. |

## Revision as of 11:27, 5 October 2017

صنف أو مجموعة الفضاء (*Ar*); Groupe d'espace (*Fr*); Raumgruppe (*Ge*); Gruppo spaziale (*It*); 空間群 (*Ja*); Кристаллографическая группа (*Ru*); Grupo espacial (*Sp*).

The symmetry group of a three-dimensional crystal pattern is called its **space group**. In *E*^{2}, the symmetry group of a two-dimensional crystal pattern is called its **plane group**. In *E*^{1}, the symmetry group of a one-dimensional crystal pattern is called its **line group**.

To each crystal pattern belongs an infinite set of translations **T**, which are symmetry operations of that pattern. The set of all **T** forms a group known as the **translation subgroup** *T* of the space group *G* of the crystal pattern. *T* is an Abelian group and a normal subgroup of the space group. The factor group *G/T* of a space group *G* and its translation subgroup is isomorphic to the point group *P* of *G*.

## See also

- Fixed-point-free space groups
- Symmorphic space groups
- Chapter 1.3 of
*International Tables for Crystallography, Volume A*, 6th edition