According to the maximum symmetry of their faces; the systems are cubic (isometric), hexagonal/trigonal (regarded as a single system), tetragonal, orthorhombic, monoclinic, and triclinic. Each system is defined by relative lengths and orientation of its three crystallographic axes. These axes are imaginary lines that pass through the center of an ideal crystal. Crystal systems, and subgroups called classes, are also defined by the crystals’ axes of symmetry. Crystals in any single crystal system can assume a variety of shapes.
Cubic crystals have three crystallographic axes at right angles of equal length, and four threefold axes of symmetry. The main forms within this system are: cube, octahedron, and rhombic dodecahedron. Minerals that crystallize in the cubic system include halite, copper, gold, silver, platinum, iron, fluorite, leucite, diamond, garnet, spinel, pyrite, galena, and magnetite. The cubic system is also sometimes known as the isometric system.
Tetragonal crystals have three crystallographic axes at right angles—two are equal in length, and the third is longer or shorter than the other two. They have one principal, fourfold axis of symmetry. Tetragonal crystals have the look of square prisms. Some of the minerals that crystallize in the tetragonal system are: rutile, calomel, cassiterite, zircon, chalcopyrite, and wulfenite.
HEXAGONAL AND TRIGONAL
Some crystallographers consider that there are seven crystal systems rather than six, separating the haxagonal from the trigonal crystals. Both heaxagonal and trigonal crystals have three crystallographic axes of equal length, set at 120 degrees to one another, and a fourth, perpendicular to the plane of the other three axes. They differ from one another in that triagonal crystals have only threefold symmetry, whereas hexagonal crystals have sixfold symmetry. Minerals that crystalize in the hexagonal system include: beryl (emerals and aquamarine, yes they are both beryl!), and apatite. Some of the minerals that crystallize in the trigonal system are: calcite, quartz, and tourmaline.
Monoclinic Crystals have three crystallographic axes of unequal length. One is at a right angles to the other two; these two axes are not perpendicular to each other, although they are the same plane. The crystals have one twofold axis of symmetry. More minerals crystallize in the monoclinic system than in any other system. The term “monoclinic” means “one incline”. Minerals that crystallize in the monoclinic system include: gypsum, borax, orthoclase, muscovite, clinopyroxene, jadeite, azurite, malachite, orpiment, and realgar.
Crystals in the orthorhombic stetem have three crystallographic axes at right angles, all of which are unequal in length. The crystals have three twofold axes of symmetry. The name “orthorhombic” means “perpendicular parallelogram”. Minerals that crystallize in the orthorhombic system include: olivine, aragonite, topaz, marcasite, and barite.
Triclinic crystals have the least symmetrical shape of all crystals. They have three crystallographic axes of unequal length, which are inclined at angles of less than 90 degrees to one another. The orientation of a triclinic crystal is arbitrary. Minerals that crystallize in the triclinic system include: albite, anorthite, kaolin, kyanite, and microline.