The monoclinic system of minerals refers to those that have all axes of unequal length and have a symmetry of 2/m, 2, or m by the Hermann-Mauguin system of notation. In this notation, "m" indicates a mirror image symmetry and "2" indicates 2-fold rotation symmetry. There are three types of monoclinic symmetry: sphenoidal, domatic and prismatic.
The sphenoidal class has a symmetry of 2 (2-fold rotation). This class is of symmetry is much less common than the prismatic class. An example of a sphenoidal mineral is chalcopyrite, which has a hardness of four and poor cleavage in one direction.
The domatic class has a symmetry of m (mirror image plane). This class of symmetry is less common than the prismatic class, but more common than the sphenoidal class. An example of a domatic mineral is antigorite, which has a hardness of three to five and no cleavage.
The prismatic class is the most common of the monoclinic system and has a symmetry of 2/m. Some examples of prismatic minerals are orthoclase, which has a hardness of six with two planes of good cleavage, augite, which has a hardness of five to six with cleavage in two directions, gypsum, which has a hardness of two with perfect cleavage in one direction and distinct cleavage in two other directions, tremolite, which has a hardness of five or six with perfect cleavage in two directions and coesite, which is an SiO2 polymorph with a hardness of eight and no cleavage.