Lattice systems are a grouping of crystal structures according to the point groups of their lattice. All crystals fall into one of seven lattice systems. They are related to, but not the same as the seven crystal systems. 
The most symmetric, the cubic or isometric system, has the symmetry of a cube, that is, it exhibits four threefold rotational axes oriented at 109.5° (the tetrahedral angle) with respect to each other. These threefold axes lie along the body diagonals of the cube. The other six lattice systems, are hexagonal, tetragonal, rhombohedral (often confused with the trigonal crystal system), orthorhombic, monoclinic and triclinic.