The Seven Crystal Systems Explained

Every mineral that has an ordered internal structure — every crystalline mineral — belongs to one of seven crystal systems. These systems are defined by the symmetry of the crystal's internal atomic arrangement, expressed in terms of three or four crystallographic axes and the angles between them. Understanding the crystal systems is foundational to crystallography and provides the framework for understanding why minerals look the way they do.

The cubic system, also called the isometric system, has the highest symmetry of all seven systems. Its defining feature is three mutually perpendicular axes of equal length (a = b = c, all angles = 90°). The high symmetry means that cubic crystals look the same from multiple directions. Common crystal forms include the cube (six square faces), the octahedron (eight triangular faces), the dodecahedron (twelve diamond-shaped faces), and various combinations of these. The symmetry elements of the cubic system include four three-fold rotation axes (one through each pair of opposite octahedral faces), three four-fold axes, six two-fold axes, and mirror planes. Minerals that crystallize in the cubic system include diamond, garnet (almandine, grossular, pyrope), pyrite, galena, halite, fluorite, magnetite, and gold. The cubic system's high symmetry often results in crystals that appear to have no preferred growth direction.

The tetragonal system has three mutually perpendicular axes, but only two are equal (a = b ≠ c, all angles = 90°). The unique c-axis (usually longer or shorter than the a and b axes) gives tetragonal crystals a characteristic elongated or flattened appearance along one direction. The four-fold symmetry axis runs along c. Common forms include tetragonal prisms, pyramids, and dipyramids. Zircon, rutile, cassiterite (tin oxide), vesuvianite, and apophyllite are familiar tetragonal minerals. Zircon crystals — stubby tetragonal prisms with pyramidal terminations — are among the most recognizable products of this system.

The orthorhombic system has three mutually perpendicular axes of all different lengths (a ≠ b ≠ c, all angles = 90°). Three two-fold rotation axes run along the crystallographic axes, giving the system its characteristic asymmetry in all three dimensions. Orthorhombic crystals are commonly tabular (flattened along one axis), prismatic, or equant. Olivine, topaz, barite, sulfur, aragonite, and celestine are orthorhombic. Olivine — the most abundant mineral in Earth's upper mantle — crystallizes as equant to short-prismatic grains in this system.

The hexagonal system is characterized by four axes: three equal horizontal axes (a1, a2, a3) at 120° to each other, and one unique vertical axis (c) perpendicular to all three. The system's defining element is a six-fold rotation axis along c. Hexagonal minerals develop characteristic six-sided prisms with flat (basal) or pyramidal terminations. Beryl (including emerald and aquamarine), apatite, and molybdenite are hexagonal. The perfect hexagonal columns of beryl — sometimes reaching enormous size in pegmatites — are one of the most immediately recognizable crystal habits in mineralogy.

The trigonal system (sometimes treated as a subsystem of hexagonal) is distinguished from hexagonal by having a three-fold, rather than six-fold, rotation axis. Many important minerals crystallize in the trigonal system: quartz, calcite, dolomite, tourmaline, corundum (sapphire and ruby), and rhodochrosite. Quartz crystals are classic trigonal specimens — six-sided prisms capped by six-faced rhombohedral terminations. The slight asymmetry of quartz faces (the presence of small rhombohedral faces alternating with the main prism faces) reflects the three-fold symmetry and is responsible for quartz's piezoelectric properties.

The monoclinic system has three unequal axes, with two perpendicular to each other and one inclined (a ≠ b ≠ c, α = γ = 90°, β ≠ 90°). The single two-fold rotation axis and mirror plane of the monoclinic system result in a characteristic asymmetry. Despite having the least symmetry of the systems with perpendicular base axes, monoclinic is the most common crystal system among all known minerals. Orthoclase feldspar, gypsum, epidote, malachite, azurite, and most of the mica group are monoclinic. The perfect flat sheets of mica — a consequence of its one perfect cleavage — are a monoclinic crystal's most recognizable feature.

The triclinic system has the lowest symmetry of all seven systems: three unequal axes at unequal angles (a ≠ b ≠ c, α ≠ β ≠ γ ≠ 90°). The only symmetry element possible in triclinic crystals is an inversion center (or no symmetry at all). Despite the apparent lack of symmetry, many important rock-forming minerals are triclinic: plagioclase feldspars (albite to anorthite), kyanite, and turquoise. The characteristic grid of fine parallel lines visible on the flat cleavage faces of plagioclase feldspars — called polysynthetic twinning — is a direct consequence of the triclinic crystal system and the tendency for plagioclase to form repeated twin lamellae.