International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 1.1, p. 5

Consider four faces of a crystal that belong to the same zone in consecutive order: , , , and . The angles between the ith and the jth face normals are designated . Then the Miller formulae relate the indices of these faces to the angles : with If all angles between the face normals and also the indices for three of the faces are known, the indices of the fourth face may be calculated. Equation (1.1.4.1) cannot be used if two of the faces are parallel.
From the definition of , , and , it follows that all fractions in (1.1.4.1) are rational: Therefore, (1.1.4.1) may be rearranged to This equation allows the determination of one angle if two of the angles and the indices of all four faces are known.