A general procedure is given for obtaining the algebraic expressions of the irreducible bases for any molecule with icosahedral symmetry from those for the molecule B12H12, which have been obtained using the symmetrized boson representation. As an illustration, concise algebraic expressions of the irreducible bases for the molecules C60 are derived for the most general case; those for any specific case can be derived from them easily without a projection procedure. Copyright 1997 Academic Press. Copyright 1997Academic Press