Abstract: On the basis of symmetry and geometry characters of Platonic polyhedrons, thebounding properties of the molecules with platonic polyhedron symmetry are discussed, andthe geometrical relationship is discribed between Platonic polyhedrons and frameworks ofcluster molecules with high symmetry, especially between Platonic polyhedrons andfullerenes.

Key words: Platonic polyhedron, Fullerenes, Symmetry of regular polyhedron