Group theoretical applications to icosahedral fullerenes

Two problems have been studied. First, by using the structural properties of representative patch chosen for an icosahedral fullerene, the whole set of irreducible representations (IR) have been obtained for the π molecular orbitals of the fullerene. Secondly, on starting with the π electronic energy levels of fullerenes Cn (IH, n = 60 k2) and Cn (Ih n = 20 k2) calculated using the Hückel approximation, their parities have been determined with the aid of a table in which the decomposition of the spherical harmonics into the IR of the Ih group have been listed.