Double group of the icosahedral group (Ih) and its application to fullerenes

The character table of the double group of the icosahedral group, Ih2 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.