A linear equation for products of normalized structure factors. II. Tensor formalism

New, finite and exact relationships between products of two normalized structure factors, with coefficients which are a function of the squared moduli of structure factors, are presented. The equations allow new linear relationships between the cosine and sine of triple-phase invariants to be set up. The meaning of the new equations is discussed in connexion with the direct calculation of cosines of triple-phase invariants and the results show, for simple one-dimensional model structures, that it is possible to obtain exact solutions.