Characterization of twinning

A new twinning condition is derived. It is more general than Friedel's ratios [Friedel, G. (1964). Leçons de Cristallographie, p. 249, Paris: Blanchard], and it allows one to predict not only the twin laws of a crystalline species, but also the regular associations of crystals mutually oriented according to non-crystallographic rotations. The deviation suffered by the twin lattice at the composition surface is better described in terms of the new twinning condition than in terms of the twin obliquity.