The derivation of twin laws for (pseudo-)merohedry by coset decomposition

The generation of possible twin laws for (pseudo-)merohedry by left coset decomposition of the point symmetry of the crystal lattice (metric symmetry) with respect to the crystal point group is presented. Two algorithms for the generation of the system of representatives have been devised. The first produces twin laws in the form of pure rotations of 180° wherever possible, and the second associates operations in pairs related by a centre of symmetry for crystals lacking an inversion centre. The metric symmetry should be determined by means of cell reduction from the measured cell dimensions and the crystal point group derived from the assumed space group. The automatic generation of twinning operations by this algorithm greatly facilitates the testing of twinning and orientation ambiguities by way of least-squares refinement of the twin fractions.