In the extensive literature dealing with the growth twinning in crystals, two approaches have been followed. Friedel (1926) related twinning to a lattice common to both parts of the twin, while others have considered how the atoms at the junction must be packed to give substantially the same interatomic distance and bond angles as in the Z single crystal. The second approach has been adopted in this paper.

This investigation has been carried out by constructing ball-and-spoke models of the various twins. The balls constituting the boundary between the two parts of the twin have been drilled to accord with the full symmetry of the twinned crystal, while the rest of the model has the normal symmetry of the untwinned crystal. The orientation of the two sets of crystallographic axes is determined by the twin law. Only when it was possible to construct a model in which the environment of the boundary balls closely approximated to the normal environment, was the proposed atomic arrangement accepted.