A generalized ring spiral algorithm for coding fullerenes and other cubic polyhedra

The so called ring spiral algorithm is a convenient means for gen erating and representing certain fullerenes and some other cubic poly hedra In Manolopoulos and Fowler presented a fullerene on vertices without a spiral No smaller unspirable fullerene is known In the spring of using computer Gunnar Brinkmann found the smallest cubic polyhedron without a spiral It has only vertices Here we generalize the ring spiral approach in order to obtain a canon ical representation for arbitrary planar cubic polyhedra Some other questions are addressed for instance possible generalization of this method to polyhedra of higher genus and to polyhedra with vertices of arbitrary valency