# Space group

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 Revision as of 10:56, 17 May 2017 (view source)m (Style edits to align with printed edition)← Older edit Revision as of 09:19, 14 September 2017 (view source)m (Lang (Ar))Newer edit → Line 1: Line 1: - Groupe d'espace (''Fr''). Raumgruppe (''Ge''). Gruppo spaziale (''It''). 空間群 (''Ja''). + Groupe d'espace (''Fr''); Raumgruppe (''Ge''); Gruppo spaziale (''It''); 空間群 (''Ja''); صنف أو مجموعة الفضاء (''Ar''). 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'''. 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'''.

## Revision as of 09:19, 14 September 2017

Groupe d'espace (Fr); Raumgruppe (Ge); Gruppo spaziale (It); 空間群 (Ja); صنف أو مجموعة الفضاء (Ar).

The symmetry group of a three-dimensional crystal pattern is called its space group. In E2, the symmetry group of a two-dimensional crystal pattern is called its plane group. In E1, 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.