LEAPFROG TRANSFORMATIONS AND POLYHEDRA OF CLAR TYPE

The so-called leapfrog transformation that was first introduced for fu llerenes (trivalent polyhedra with 12 pentagonal faces and all other f aces hexagonal) is generalised to general polyhedra and maps on surfac es. All spherical polyhedra can be classified according to their leapf rog order. A polyhedron is said to be of Clar type if there exists a s et of faces that cover each vertex exactly once. It is shown that a fu llerene is of Clar type if and only if it is a leapfrog transform of a nother fullerene. Several basic transformations on maps are defined by means of which the leapfrog and other transformations can be accompli shed.