Irreducible bases in icosahedral group space

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.