A set of five rules, proposed by Linus Pauling in 1929, that enables the structures of many complex ionic crystals to be understood. The rules concern: (1) the radius ratio; (2) local electrical neutrality; (3) the decrease in stability when faces and edges of polyhedra are shared due to cations being close to each other; (4) the tendency for crystals with different cations that have high valence and a small coordination number not to share polyhedron elements, so as to increase the distance between highly charged cations; and (5) parsimony, the principle that the number of different constituents in a crystal tends to be small. They work well for mainly ionic crystals, such as silicates, but less well for crystals, such as sulphides, in which the bonding is mainly covalent. Even in ionic crystals, Pauling’s rules are not universally applicable. Pauling put forward his rules on the basis of empirical observations and calculations of crystal energies. A number of extensions and modifications have been proposed.