Uniqueness of rotationally invariant polyhedra classification

In the past, algorithms have been proposed that yield a classification of coordination polyhedra (coordination stars) in terms of an infinite set of rotationally invariant coefficients. It is shown that this set provides a unique characterization of the polyhedra, in the sense that two polyhedra with the same set of coefficients can always be transformed into each other by a rotation or a rotation combined with an inversion.