Geologists classify crystals into six groups based on the number of axes and the angles of the facets, or faces, on a specimen. The science of crystallography labels the six categories as isometric, tetragonal, orthorhombic, monoclinic, triclinic and hexagonal.
Each crystal has a central axis point. A cube, or isometric crystal, has three axes, all equal in length and all perpendicular to each other. The tetragonal crystal is similar, but only two axes are of equal length, creating a rectangular shape. The orthorhombic crystal has three axes, all perpendicular to each other, but each with a different length.
The monoclinic crystal has three axes, all of different lengths, with two of them perpendicular to the third. The triclinic crystal has three axes but none are perpendicular to the other and each one is a different length. Hexagonal crystals have four axes, three that are equal in length and symmetrically placed. These three are perpendicular to the fourth, which is longer.
Geologists identify many gemstones by their crystal shapes. Diamonds are isometric and are perfect for cutting into gemstones, since the cubed shape creates little waste. A variation often found is the octahedron, an elongated cube-shaped diamond. Sapphires are hexagonal in shape, having six elongated symmetrical facets and slanted perpendicular ends. Topaz crystals are orthorhombic, shaped like a rectangle but with all facets having a different length.