For computation the most convenient form to express transformation of indices attending twin gliding is that of a matrix comparable to matrices used in connection with changes in the axes of reference. The matrix can be obtained by the usual equations, first derived by Mügge (1889a, p. 286–294), or directly from the changes of indices of a suitable set of three faces. These can usually be chosen by inspection when the elements of twin gliding are established.

The reciprocal lattice and the gnomonic projection are used to represent the several types of twin gliding.

Transformation of crystal forms, of the lattice, and of the crystal structure are illustrated by stereographic projections and diagrams. Geometric criteria can sometimes be used not only to determine the possibility of twin gliding but also to decide the sense of the glide.

Simple shear describes twin gliding megascopically, but this concept requires modification hi describing known cases of atom movements. Structures at the moving twin boundary are related to polymorphs of the crystal undergoing gliding in certain cases.

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