are vertex-linked mixed chains of alternating octahedra and tetrahedra. The tetrahedra have a phosphorus ion P in the middle, and oxygen ions O at each of the four vertices, and the octahedra have an aluminium ion Al in the middle surrounded by six oxygen ions O, as in the octahedral chains. At each linked vertex one O is shared between a tetrahedron and an octahedron, and each tetrahedron and octahedron must have two linked vertices to form the mixed chain. Each octahedral chain is flanked by two mixed chains, one on either side, linked through the vertices of the chains, making an infinite triple chain. The triple chains are further interlinked by yet more phosphorus tetrahedra (not the ones in the mixed chains), which share vertices with both kinds of octahedra in the octahedral chains, and with the aluminium octahedra in the mixed chains. Water molecules (H2O) and hydroxyl ions (OH) are also incorporated into this chain, giving a complex chain with composition [FeAl3(PO4)4(OH)4(OH2)2]5−. These complex chains, which are parallel to the c crystal axis, are linked in the direction of the a axis by further aluminium octahedra (not the ones in the chains) and in the direction of the b axis by further Fe octahedra, and there are more water molecules within channels in the structure, giving the final formula for vauxite as FeAl2(PO4)2(OH)2.6H2O. Crystal habit Vauxite crystals are very small and tabular, forming sub-parallel to radial aggregates and nodules. The crystals are flattened parallel to the plane containing the a and c crystal axes, and elongated in the c direction, that is along the length of the chains which are the basis of the structure. Optical properties A triclinic mineral, such as vauxite, has all three of its crystal axes of different lengths, and all three interaxial angles of different sizes, with none equal to 60°, 90° or 120°. Consequently, the material is anisotropic, and physical properties, including optical properties, vary with direction. The refractive index is the ratio of the speed of light in vacuum to the speed of light through the medium. Since this varies with the color of the light, a standard color must be chosen when refractive indices are specified. The usual standard is the yellow light from a sodium source, that has wavelength 589.3 nanometers. For an anisotropic substance the refractive index (for light of a given color) varies with direction, and for