The character table of the double group of the icosahedral group, I 2 h is derived. The correlation table for the rovibronic states as well as spin states both involving integral and half-integral spins are derived. It is shown that the spin states that correspond to half-integral and integral spins exhibit a cyclicity of 15 and 30, respectively, with respect to correlation into the double group. Applications to the spin-orbits states of metallo-fullerene are considered.