Icosahedral and tetrahedral glant and hyperfullerenes

Summary form only given. According to the geometrical relationship between an icosahedron, tetrahedron and a carbon cage cluster, a method is devised to perceive the simple mathematical formula to generate the structure of icosahedral and tetrahedral giantfullerenes. This method also allows the calculation of the number of hexagons, vertices and edges of any giant fullerenes of such I/sub h/ and T/sub d/ symmetry. The irreducible representations of 2/sub s/ and 2/sub p/ molecular orbitals of these giant fallerenes are generated, The cage diameters and the distance between two neighboring encapsulating cage in hyperfullerenes are deduced. The semiempirical EHT method is used to generated the energy gap between LUMO and HOMO of these giantfullerenes.