Difference between revisions of "Space group"
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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="orange">صنف أو مجموعة الفضاء</font> (''Ar''). <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="brown">Кристаллографическая группа</font> (''Ru''). <font color="green">Grupo espacial</font> (''Sp''). |
| − | 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