In geometry and crystallography a Bravais lattice, named afterAuguste Bravais is an infinite set of points generated by a set of discrete translation operations. A crystal is made up of one or more atoms (the basis ) which is repeated at each lattice point. The crystal then looks the same when viewed from any of the lattice points. In all, there are 14 possible Bravais lattices that fill three-dimensional space. Related to Bravais lattices are crystallographic point groups of which there are 32 and space groups of which there are 230.
A crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after any of the operations in its point group. In the classification of crystals, each point group corresponds to a crystal class .
The space group of a crystal or crystallographic group is a mathematical description of the symmetry inherent in the structure.