It was recalled that the algebraic equation for twinning involved a unimodular matrix, a general non-singular matrix, a rotation and 2 vectors. The present work generalized previous investigations by listing, for each given unimodular matrix, all of the solutions of the twinning equation. It assumed a given rotation and vector, and listed all of the solutions. Using a different approach, it assumed that a non-singular matrix was the identity and furnished all of the solutions. The latter approach was linked to elementary number theory. One observation was that the twinning equation merely required that part of the orbit of the rotation matrix be synchronized, with some other part of the orbit of the unimodular matrix, by a non-singular matrix.

On Matrix Equations of Twinning in Crystals. S.A.Adeleke: Mathematics and Mechanics of Solids, 2000, 5[4], 395-415