In the field of optical mineralogy, mineral crystals according to the internal arrangement of the component atoms, that is, in terms of the fundamental space lattices, as determined by X-ray analysis, are readily classified into six groups called crystal systems. The classification can also be made in terms of the lengths and angular relationships of imaginary lines that pass through the center of a crystal called crystal axes. Basic study of the crystals is based upon the crystal axes rather than upon the space lattices. The six crystal systems determined in optical mineralogy includes cubic or isometric, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic systems.

            The cubic crystal system has three equal and perpendicular axes. Examples of minerals classified into this system are diamonds, spinel, and garnet. Hexagonal system has four axes. Three of these are equal, horizontal, and intersect at 60 degrees. The fourth axis is perpendicular to these and therefore vertical. It is longer or shorter than the horizontal axes. Examples of minerals belonging to this group are beryl, corundum, quartz, and tourmaline. It is interesting to note that emerald and aquamarine are gem varieties of beryl, while ruby and sapphire are of corundum. Tetragonal system has three axes which intersect at right angles. The vertical axis is longer or shorter than the two equal horizontal axes. Examples of minerals belonging to this group are zircon and vesuvianite. Orthorhombic system is characterized by three perpendicular and unequal axes. Olivine and topaz belong to this group. Monoclinic system has three axes that are also unequal. Two intersect at an oblique angle, and the third is perpendicular to them. Mineral belonging to this group includes epidote, spodumene, and titanite. Triclinic system on the other hand, has three axes, all inequal, and all inclined to each other. Minerals belonging to this group include labradorite and some moonstones.

            In optical mineralogy, the classification of crystals into systems may also be made in terms of the elements of symmetry, that is, planes, axes, and center of symmetry. Based upon symmetry the six crystal systems are subdivided into thirty-two classes of symmetry. Crystals with the highest type of symmetry, that is, those most symmetrically developed, are the representative of the cubic system. Crystals with the lowest type of symmetry belong to the triclinic system.

            Certain relationships between the systems may now be pointed out. The morphological classification of crystals into systems is by no means artificial. The optical properties form another natural basis for the classification. But the crystal form and the optical characteristics depend upon the arrangement of the atoms which make up a crystal. Thus, crystals may be divided into three groups. First is the cubic crystals system. Secondly is the hexagonal and tetragonal crystal system. Lastly is the orthorhombic, monoclinic, and triclinic crystal system. In the field of optical mineralogy, when light passes through crystals of the cubic system without being resolved into two rays, these substances are singly refractive. Cubic minerals are also optically isotropic because light travels through them in the same velocity in all directions. It is important to note that amorphous substances, those which do not crystallize, are also singly refractive. All other substances are, in general, doubly refractive. That is, a ray of light upon passing through them is resolved into two rays. These crystals are optically anisotropic, for light travels through them with different velocities in different directions. Hexagonal and tetragonal substances show, however, single refraction in one direction, parallel to the vertical axis. This isotropic direction is called the optic axis. Since crystals of these systems have only one such direction, they are so called uniaxial. Substances crystallizing in the orthorhombic, monoclinic, and triclinic systems have two isotropic directions or optic axes, and are therefore called biaxial. Other distinctions serve to differentiate the systems within these groups.