  The irreducible bases in the icosahedral group space are calculated
explicitly by reducing the regular representation. The symmetry adapted bases
of the system with {\bf I} or {\bf 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
H\"{u}ckel Hamiltonians for Carbon-60 and Carbon-240 are re-calculated by the
irreducible bases.
