Bravais lattice
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In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. A Bravais lattice looks exactly the same no matter from which point one views it.
The position vectors of a Bravais lattice in three dimensions are given by
- <math>\mathbf{R} = n_1 \mathbf{a}_1 + n_2 \mathbf{a}_2 + n_3 \mathbf{a}_3,<math>
where n1, n2, and n3 are integers and a1, a2, and a3 are three non-coplanar vectors, called primitive vectors.
When classified by space group, there are 14 unique Bravais lattices in three dimensions. These can be grouped according to their crystal system, or crystallographic point group. The 14 Bravais lattices are:
| Crystal system | lattice |
| triclinic | |
| monoclinic | simple |
| centered | |
| orthorhombic | simple |
| base-centered | |
| body-centered | |
| face-centered | |
| hexagonal | |
| rhombohedral (trigonal) | |
| tetragonal | simple |
| body-centered | |
| cubic (isometric) | simple |
| body-centered | |
| face-centered | |
The Bravais lattices were studied by M. L. Frankenheim in 1842, who found that there were 15 Bravais lattices. This was corrected to 14 by A. Bravais in 1848.
See also
For a more mathematically intensive discussion, see lattice (group).de:Bravais-Gitter nl:Bravais-rooster ru:Решётка Браве