Bravais lattices, the fourteen three-dimensional geometrical lattices that characterise the possible types of translational symmetry of a crystal lattice. The Bravais lattices were established by the French crystallographer A. Bravais in 1848. A complete description of the symmetry of the atomic structure of a crystal is given by its space group of symmetry, which contains both translation operations and operations of rotation, reflection and inversion. A Bravais lattice is produced by applying the translation operations alone to an arbitrary point of the crystal, and the system of lattice points is derived from that point. A distinction is drawn between primitive Bravais lattices, in which the points lie only at the vertices of the elementary parallelepipeds, face-centred ones (at the vertices and at the centres of all the faces), body-centred ones (at the vertices and at the centre of the parallelepipeds) and base-centred ones (at the vertices and at the centres of two opposite faces) (Fig.).
The Bravais lattices are classified by the symmetry of the unit cell, by the relations that follow from it between the edges a, b, c and the angles α, β, γ of the parallelepiped, and also by their centring. If only the first of these is taken into account, all crystals fall into 7 crystal systems, among which the 14 Bravais lattices are distributed. The concept of a “Bravais lattice” is used in describing the atomic structure of crystals, by stating that the centres of particular atoms lie at the points of a definite Bravais lattice. In the simplest cases (for example, in metals) the structure is described by a single Bravais lattice. A complex structure whose unit cell contains several atoms can be described as several Bravais lattices “pushed” one into another.