Difference between revisions of "Space group"
From Online Dictionary of Crystallography
BrianMcMahon (talk | contribs) m (Tidied translations.) |
(synonym) |
||
| Line 2: | Line 2: | ||
| − | 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''' (also known as ''wallpaper 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. The [[factor group]] ''G/T'' of a space group ''G'' and its translation subgroup is isomorphic to the [[point group]] ''P'' of ''G''. | 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''. | ||
Latest revision as of 13:37, 19 February 2021
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 E2, the symmetry group of a two-dimensional crystal pattern is called its plane group (also known as wallpaper 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