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Difference between revisions of "Space group"

From Online Dictionary of Crystallography

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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'''.
  
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.
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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==
 
==See also==

Revision as of 12:22, 14 April 2017

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 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.

See also