Lattice system: Difference between revisions
From Online Dictionary of Crystallography
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== Lattice systems in two and three dimensions == | == Lattice systems in two and three dimensions == | ||
In two-dimensional space there exist four lattice systems: | In two-dimensional space there exist four lattice systems: | ||
* | * oblique | ||
* | * rectangular | ||
* | * square | ||
* hexagonal | * hexagonal | ||
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== Note == | == Note == | ||
In previous editions of ''Volume A'' of ''International Tables of Crystallography'' (before 2002), the lattice systems were called ''Bravais systems''. | In previous editions of ''Volume A'' of ''International Tables of Crystallography'' (before 2002), and in previous editions of ''Volume E'' of ''International Tables of Crystallography'', the lattice systems were called ''Bravais systems''. | ||
== See also == | == See also == | ||
Revision as of 12:41, 6 July 2025
Système réticulaire (Fr). Gittersystem (Ge). Sistema reticolare (It). 格子系 (Ja).
Definition
A lattice system of space groups contains complete Bravais classes. All those Bravais classes which intersect exactly the same set of geometric crystal classes belong to the same lattice system.
Alternative definition
A lattice system of space groups contains complete Bravais classes. All those Bravais classes belong to the same lattice system for which the Bravais arithmetic classes belong to the same (holohedral) geometric crystal class.
Lattice systems in two and three dimensions
In two-dimensional space there exist four lattice systems:
- oblique
- rectangular
- square
- hexagonal
In three-dimensional space there exist seven lattice systems:
- triclinic
- monoclinic
- orthorhombic
- tetragonal
- rhombohedral
- hexagonal
- cubic
Note that the adjective trigonal refers to a crystal system, not to a lattice system. Rhombohedral crystals belong to the trigonal crystal system, but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system.
Note
In previous editions of Volume A of International Tables of Crystallography (before 2002), and in previous editions of Volume E of International Tables of Crystallography, the lattice systems were called Bravais systems.
See also
- Bravais class
- Chapter 1.3.4.4.2 of International Tables for Crystallography, Volume A, 6th edition