Ten geometrical parameters are required to specify an arbitrary planar interface between crystalline solids. Seven parameters describe the translation and rotation operators which characterize the spatial relation of the two crystals meeting at the interface. An additional three parameters describe the position of the interface relative to both crystals.

Methods were derived for determining interfacial symmetry groups as a function of the ten parameters and of the symmetry groups of the individual crystals. The first step is to determine the symmetry of the dichromatic pattern (dcp), an imaginary construct consisting of two infinite inter penatrated crystals exhibiting the relative rotation and translation characteristic of the interface. The symmetry of the dop was described within the framework of the Shubnikov, or black and white, groups. Interfacial symmetry can than be derived as a function of dcp symmetry and of the three parameters describing interface location.

Interfacial symmetry groups can be used to derive constraints on physical properties of interfaces and of polycrystalline aggregates. The following applications were made:​

• The group of the Wulff plot was derived for a crystal in a crystalline, rather than isotropic medium. This group defines morphological constraints in solid state phase transformations and in eutectic solidification. Microstructures observed in metals and ceramics were consistent with the theory.
• Symmetry dictates positions of extrema in interfacial properties as the geometrical parameters are varied. Orientation relationships observed in phase transformations in metals and ceramics were considered.
• Symmetry constraints on the forms of interfacial tensor properties were discussed, as were uses of symmetry in the analysis of quantum mechanical properties of interfaces. Applications of the theory were made to the study of crystal field splitting of electronic energy levels of impurity atoms segregated at interfaces, and to the interfacial vibrational mode problem.