In well-formed crystals, the symmetrically arranged faces reflect the internal arrangement of atoms. The symmetry of individual crystals is determined by reference to three elements. The plane of symmetry (also called the ‘mirror plane’ or ‘symmetry plane’) is a plane by which the crystal may be divided into two halves which are mirror images of each other. The axis of symmetry is a line about which a crystal may be rotated through 360°/n until it assumes a congruent position; n may equal 2, 3, 4, or 6 (but not 1), depending on the number of times the congruent position is repeated. These correspond respectively to 2-fold (diad), 3-fold (triad), 4-fold (tetrad), and 6-fold (hexad) axes. The centre of symmetry is a central point which is present when all faces or edges occur in parallel pairs on opposite sides of the crystal. Using these elements of symmetry, crystallographers have recognized 32 crystal classes and seven crystal systems. Symmetry is highest (high symmetry) in the cubic system, where many elements are repeated, and lowest (low symmetry) in the triclinic system, where only a centre of symmetry may be present (i.e. there may be no plane or axis of symmetry).

Crystal symmetry