Continuous symmetry measures: A note in proof of the folding/unfolding method

The measurement of the degree of symmetry proved to be a useful tool in the prediction of quantitative structural-physical correlations. These measurements have been based, in the most general form, on the folding/unfolding algorithm, for which we provide here a new and simpler proof. We generalize this proof to the case of objects composed of more than one (full) orbit. An important practical issue we consider is the division of the graph into symmetry orbits and the mapping of the symmetry group elements onto the points of the graph. The logical constraints imposed by the edges of the graph are reviewed and used for the successful resolution of the coupling between different orbits.