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="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="orange">صنف أو مجموعة الفضاء</font> (''Ar''). |
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 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.
See also
- Fixed-point-free space groups
- Symmorphic space groups
- Chapter 1.3 of International Tables for Crystallography, Volume A, 6th edition