GEOMETRY AND ORBITAL SYMMETRY RELATIONSHIPS OF GIANT AND HYPERFULLERENES - C240, C540, C960 AND C1500

From the truncation of the triangular faces of an icosahedron, a metho d is devised to perceive the geometrical relationship between the (gia nt) fullerene components of hyperfullerenes: C60, C240, C540, C960 and C1500. This method also allows the calculation of the number of hexag onal faces (besides the 12 pentagonal faces), vertices and edges of an y giant fullerene of such I(h) symmetry. From symmetry considerations, the irreducible representations of all of the sigma and pi molecular orbitals of such giant fullerenes are deduced. The cage diameters and the distance between two neighboring encapsulating cage fullerenes are estimated. the overlap integrals between nearest neighbor carbon atom s based on their orientational relationship are calculated. The relati ve sizes of the integrals may be used to estimate the relative bonding strength and interaction potentials of these fullerenes.