Bravais lattice

Summary

A Bravais lattice is the set of all integer combinations of $n$ linearly independent vectors in $\R^n$. Physics uses it to describe the translation symmetry of a crystal. As a set it is a lattice in $\R^n$, and the crystal is obtained by placing the same group of atoms at every lattice point. Bravais lattices are sorted into types by their symmetry: there are $5$ types in the plane and $14$ in space. The reciprocal lattice and the Brillouin zone are built from it.