# Difference between revisions of "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="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''). | ||

− | 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'''. |

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. | 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. |

## Revision as of 14:35, 22 December 2016

Groupe d'espace (*Fr*); Raumgruppe (*Ge*); Gruppo spaziale (*It*); 空間群 (*Ja*).

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.

## See also

- Fixed-point-free space groups
- Symmorphic space groups
- Chapter 8 of the
*International Tables for Crystallography, Volume A*