Fig. 1.—Cubo-Octahedra.

The development of natural faces on a crystal is far from being haphazard, but is governed by the condition that the angles between similar faces, whether on the same crystal or on different crystals, are equal, however varying may be the shapes and the relative sizes of the faces (Fig. 1), and by the tendency of the faces bounding the crystal to fall into series with parallel edges, such series being termed zones. Each species has a characteristic type of crystallization, which may be referred to one of the following six systems:—

1. Cubic.—Crystals in this system can be referred to three edges, which are mutually at right angles, and in which the directional characters are identical in value. These principal edges are known as axes. Some typical forms are the cube (Fig. 2), characteristic of fluor; the octahedron (Fig. 3), characteristic of diamond and spinel; the dodecahedron (Fig. 4), characteristic of garnet; and the triakisoctahedron, or three-faced octahedron (Fig. 5).

Fig. 2.—Cube.

Fig. 3.—Octahedron.

Fig. 4.—Dodecahedron.

All crystals belonging to this system are singly refractive.