Orientations of reflection-rotation groups

The authors extend the work of a previous paper (1980) in which they showed that some of the phase choices in the 3jm factors of certain point group embeddings affect the orientation of the symmetry axes. The occurrence of such choices is unpredictable and their effect is sometimes subtle but once a set of 3jm factors has been calculated they can determine the orientations of the symmetry axes and mirror planes and investigate how these orientations vary with the phase choices. The properties of the reflection-rotation groups are obtained from the the isomorphic pure rotation groups but care is necessary in interpreting the effects of the corresponding operations of, for example, D3 and C3v.

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