Every crystal class is a member of one of the six crystal systems. These systems include the isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic crystal systems. The hexagonal crystal system is further broken down into hexagonal and rhombohedral divisions.

Every crystal class which belongs to a certain crystal system will share a characteristic symmetry element with the other members of its system. For example, all crystals of the isometric system possess four 3-fold axes of symmetry which proceed diagonally from corner to corner through the center of the cubic unit cell. In contrast, all crystals of the hexagonal division of the hexagonal system possess a single six-fold axis of rotation.

In addition to the characteristic symmetry element, a crystal class may possess other symmetry elements which are not necessarily present in all members of the same system. The crystal class which possesses the highest possible symmetry or the highest number of symmetry elements within each system is termed the holomorphic class of the system. For example, crystals of the holomorphic class of the isometric system possess inversion symmetry, three 4-fold axes of rotational symmetry, the characteristic set of four 3-fold axes of rotational symmetry which is indicative of the isometric crystal system, six 2-fold axes of rotational symmetry, and nine different mirror planes. In contrast, a crystal which is not a member of the holomorphic class yet still belongs to the isometric system may possess only three 2-fold axes of rotational symmetry and the characteristic four 3-fold axes of rotational symmetry.

The crystal system of a mineral species may sometimes be determined in the field by visually examining a particularly well-formed crystal of the species. Below is a list of the seven crystal systems with a brief description. For more information about each system, click the name.

Amorphous

Isometric (Cubic)

Hexagonal

Monoclinic

Orthorhombic

Tetragonal

Triclinic