Difference between revisions of "Bravais arithmetic class"
From Online Dictionary of Crystallography
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| − | <font color="blue">Classe de Bravais </font>(''Fr''). < | + | <font color="blue">Classe arithmétique de Bravais</font> (''Fr''). <font color="red">Bravais Arithmetische Klasse</font> (''Ge''). <font color="black">Classe aritmetica di Bravais</font> (''It''). <font color="purple">ブラベー代数的類</font> (''Ja''). <font color="green">Clase aritmética de Bravais</font> (''Sp''). |
== Definition == | == Definition == | ||
| − | An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class'' | + | An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class''. |
| − | Each lattice is associated with a Bravais class, and each matrix group of a Bravais class represents the point group of a lattice referred to an | + | Each lattice is associated with a Bravais arithmetic class, and each matrix group of a Bravais arithmetic class represents the point group of a lattice referred to an appropriate primitive basis. |
| − | There exist 5 Bravais classes in two dimensions: | + | There exist 5 Bravais arithmetic crystal classes in two dimensions: |
| − | * | + | * <math> 2p </math> |
| − | * | + | * <math> 2mmp </math> |
| − | * | + | * <math> 2mmc </math> |
| − | * | + | * <math> 4mmp </math> |
| − | * | + | * <math> 6mmp </math> |
| − | There exist 14 Bravais classes in three dimensions: | + | There exist 14 Bravais arithmetic crystal classes in three dimensions: |
| − | * <math>{\bar 1}</math> | + | * <math> {\bar 1}P </math> |
| − | * 2/ | + | * <math> 2/mP </math> |
| − | * 2/ | + | * <math> 2/mC </math> |
| − | * | + | * <math> mmmP </math> |
| − | * | + | * <math> mmmC </math> |
| − | * | + | * <math> mmmF </math> |
| − | * | + | * <math> mmmI </math> |
| − | * 4/ | + | * <math> 4/mmmP </math> |
| − | * 4/ | + | * <math> 4/mmmI </math> |
| − | * <math>{\bar 3}</math> | + | * <math> {\bar 3}mR </math> |
| − | * 6/ | + | * <math> 6/mmmP </math> |
| − | * | + | * <math> m{\bar 3}mP </math> |
| − | * | + | * <math> m{\bar 3}mF </math> |
| − | * | + | * <math> m{\bar 3}mI </math> |
== See also == | == See also == | ||
| − | + | *[[Bravais class]] | |
| + | *Chapter 1.3.4.4 of ''International Tables for Crystallography'', ''Volume A'', 6th edition | ||
[[category: Fundamental crystallography]] | [[category: Fundamental crystallography]] | ||
Latest revision as of 15:24, 6 July 2025
Classe arithmétique de Bravais (Fr). Bravais Arithmetische Klasse (Ge). Classe aritmetica di Bravais (It). ブラベー代数的類 (Ja). Clase aritmética de Bravais (Sp).
Definition
An arithmetic crystal class with matrix group of lattices is called a Bravais arithmetic crystal class.
Each lattice is associated with a Bravais arithmetic class, and each matrix group of a Bravais arithmetic class represents the point group of a lattice referred to an appropriate primitive basis.
There exist 5 Bravais arithmetic crystal classes in two dimensions:
- [math] 2p [/math]
- [math] 2mmp [/math]
- [math] 2mmc [/math]
- [math] 4mmp [/math]
- [math] 6mmp [/math]
There exist 14 Bravais arithmetic crystal classes in three dimensions:
- [math] {\bar 1}P [/math]
- [math] 2/mP [/math]
- [math] 2/mC [/math]
- [math] mmmP [/math]
- [math] mmmC [/math]
- [math] mmmF [/math]
- [math] mmmI [/math]
- [math] 4/mmmP [/math]
- [math] 4/mmmI [/math]
- [math] {\bar 3}mR [/math]
- [math] 6/mmmP [/math]
- [math] m{\bar 3}mP [/math]
- [math] m{\bar 3}mF [/math]
- [math] m{\bar 3}mI [/math]
See also
- Bravais class
- Chapter 1.3.4.4 of International Tables for Crystallography, Volume A, 6th edition