Inst High Energy Phys, Beijing 100039, Peoples R China
; Univ Three Gorges, Dept Phys, Yichang 443000, Peoples R China
; Tianjin Normal Univ, Dept Phys, Tianjin 300074, Peoples R China
The irreducible bases in the icosahedral group space are calculated explicitly by reducing the regular representation. The symmetry-adapted bases of the system with I or I-h symmetry can be calculated easily and generally by applying those irreducible bases to wavefunctions of the system, if they are not vanishing. As examples, the submatrices of the Huckel Hamiltonians for carbon-60 and carbon-240 are recalculated by the irreducible bases.