According to the similarity of their symmetry elements, thirty-two classes are grouped into seven crystal systems: isometric (cubic) system, tetragonal system, hexagonal system, trigonal system (subdivision of the hexagonal system, second North American school of crystallography). , called rhombohedral hexagonal system), orthorhombic system, monoclinic system and triclinic system. Applying the symmetry operations on all possible reticular planes (potential crystal faces) in the seven crystalline systems, according to the 32 symmetry classes, only 48 geometric shapes are possible to be obtained.
