Twinning and symmetry

Twins of the first and second kind are found to be indistinguishable in crystals of high symmetry. A basis for the symmetry dependence is found which will delineate some situations where this is expected. Namely, when the space group of the twinned crystals is the same and contains the transformation operator which relates the two crystals, and when the twinning operator contains no translation, such compound twins are expected. Furthermore, the two invariant planes and directions are members of the same families of planes and directions, respectively. Otherwise, either compound twins are found where the invariant planes are not members of the same family or the compound twin transforms into the two separate kinds