A lattice system is a class of point lattices having the same type of full point group. This group consists of the orthogonal transformations fixing a chosen lattice point and preserving the point lattice. In three dimensions, the seven lattice systems are triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic. They contain 1, 2, 4, 2, 1, 1, and 3 Bravais lattice types, respectively (Grimmer 2015, pp. 144-145).
The shape of an arbitrarily chosen unit cell alone does not determine the lattice system. Special metric values can move a point lattice into a system with higher symmetry.
