An ellipsoid which represents geometrically the different vibration directions in a mineral and illustrates conceptually the optical features of a crystal. The origin is a point lying at the centre of the ellipsoid and the axes of the ellipsoid are proportional in length to the refractive indices of beams of light vibrating at right angles along them. These axes are commonly termed X, Y, and Z, or n_α‎, n_β‎, and n_γ‎, for orthorhombic, monoclinic, or triclinic minerals. Tetragonal, hexagonal, and trigonal minerals are represented by an indicatrix with one principal section circular; and the cubic minerals are represented by an indicatrix (the isotropic indicatrix) which is a sphere with all axes equal. Measurements of the elliptical plane sections give optical properties which aid specific identification of a mineral. See optic axis.