All gemstones are crystalline structures made from a mixture of different elemental compounds. The shape of a crystal is based on the atomic structure of these elemental building blocks. Atoms within a mineral are arranged in an ordered geometric pattern which determine its "crystal structure". A gem's crystal structure will determine a its symmetry, optical properties, cleavage and geometric shape. The recipe or mixture of these compounds becomes the blueprint for how the crystal will grow. This growth pattern is call a crystal's "habit."
The "unit cell" is the smallest divisible unit of a mineral with symmetrical characteristics unique to a crystalline structure. A structure's "unit cell" is a spatial arrangement of atoms which is tiled in three-dimensional space to form the crystal. The unit cell is determined by its lattice parameters, the length of the cell edges and the angles between them, while the positions of the atoms inside the unit cell are described by the set of atomic positions (xi,yi,zi) measured from a lattice point.
The crystal system is a grouping of crystal structures that are categorized according to the axial system used to describe their "lattice". A crystal's lattice is a three dimensional network of atoms that are arranged in a symmetrical pattern. Each crystal system consists of a set of three axes in a particular geometrical arrangement. The seven unique crystal systems, listed in order of decreasing symmetry, are: 1. Isometric System, 2. Hexagonal System, 3. Tetragonal System, 4. Rhombohedric (Trigonal) System, 5. Orthorhombic System, 6. Monoclinic System, 7. Triclinic System.
The Seven Crystal Systems
The Cubic crystal system is also known as the "isometric" system. The Cubic (Isometric) crystal system is characterized by its total symmetry. The Cubic system has three crystallographic axes that are all perpendicular to each other and equal in length. The cubic system has one lattice point on each of the cube's four corners.
The Hexagonal crystal system is has four crystallographic axes consisting of three equal horizontal or equatorial (a, b, and d) axes at 120º, and one vertical (c) axis that is perpendicular to the other three. The (c) axis can be shorter or longer than the horizontal axes.
A Tetragonal crystal is a simple cubic that is stretched along its (c) axis to form a rectangular prism. The Tetragonal crystal will have a square base and top, but a height that is taller. By continuing to stretch the "body-centered" cubic one more Bravais lattice of the Tetragonal system is constructed.
A Rhombohedron (aka Trigonal) has a three-dimensional shape that is similar to a cube that has been compressed to one side. Its form is considered prismatic, as all faces are parallel to each other. The faces that are not square are called "rhombi." A rhombohedral crystal has six faces or rhombi, 12 edges, and 8 vertices. If all of the non-obtuse internal angles of the faces are equal (flat sample, below), it can be called a trigonal trapezohedron.
Minerals that form in the Orthorhombic (aka Rhombic) crystal system have three mutually perpendicular axes, all with different or unequal lengths.
Crystals that form in the Monoclinic System have three unequal axes. The (a) and (c) crystallographic axes are inclined toward each other at an oblique angle, and the (b) axis is perpendicular to a and c. The (b) crystallographic axis is called the "ortho" axis.
Crystals that form in the Triclinic System have three unequal crystallographic axes, all of which intersect at oblique angles. Triclinic crystals have a 1-fold symmetry axis with virtually no symmetry and no mirrored planes.