A buckminsterfullerene molecule C60 15 belongs to the icosah

A buckminsterfullerene molecule, C60 (15), belongs to the icosahedral
point group. What is the maximum possible degree of degeneracy of its orbitals?

Solution

linear combination of the fivefold degenerate H.., an the two three-fold degenergate, T1u and T2u irreducible representations of the icosahedral group. Group theory doesn\'t predict the order of the levels, but shows that if the five-fold degenerate level is placed lowest, an energy level diagram that captures the essentials of the known electronic structure of C60 is obtained.ie maximum degree of degeneracy===5.