Numbering the crystallographic variants in phase transformation

In phase transformation one initial orientation gives rise to several final orientations called crystallographic variants. In this paper it is shown that the number of physically distinct variants depends not only on the lattice symmetry of the initial phase but also on the mutual orientation relations between the lattices. This number is lower than the order of the rotational symmetry group when commutation relations exist between some rotations of the rotational symmetry group and rotations which describe the mutual orientations between lattices. Different examples are given for illustration.