☞ The systems of crystallization are the several classes to which the forms are mathematically referable. They are most simply described according to the relative lengths and inclinations of certain assumed lines called axes; but the real distinction is the degree of symmetry characterizing them. 1. , or has the axes all equal, as in the cube, octahedron, etc. 2. , or has a varying vertical axis, while the lateral are equal, as in the right square prism. 3. , or has the three axes unequal, as in the rectangular and rhombic prism. In this system, the lateral axes are called, respectively, macrodiagonal and brachydiagonal. – The preceding are erect forms, the axes intersecting at right angles. The following are oblique. 4. , having one of the intersections oblique, as in the oblique rhombic prism. In this system, the lateral axes are called respectively, clinodiagonal and orthodiagonal. 5. , having all the three intersections oblique, as in the oblique rhomboidal prism. There is also: 6. (one division of which is called Rhombohedral), in which there are three equal lateral axes, and a vertical axis of variable length, as in the hexagonal prism and the rhombohedron.

☞ The Diclinic system, sometimes recognized, with two oblique intersections, is only a variety of the Triclinic.