The crystal-field splitting of rare-earth ions in icosahedral symmetry is treated by group-theoretical and numerical methods. From the crystal-field Hamiltonian, which is governed by only one crystal-field parameter, the crystal-field splitting schemes of all rare-earth ions in their Hund's-rule ground state are derived. It is shown that these schemes are expected to survive in quasicrystals as well as in metallic glasses. The derived temperature dependence of the surplus static susceptibility and specific heat, as generated by the icosahedral crystal-field splitting, is discussed and plotted for selected cases.