= Solution
\b[The highest expected orbital degeneracy is five.] Ideal <buckminsterfullerene> has <Ih molecular point group> symmetry. Its irreducible orbital representations include five-dimensional $H_g$ and $H_u$ representations; no single-valued orbital irrep has higher dimension.
This counts distinct spatial <molecular orbitals>. It does not multiply by electron spin, and it excludes accidental coincidences between unrelated irreps. In a real environment, symmetry lowering can split these degeneracies.<Tables for Group Theory by P. W. Atkins and others>[Printed page 17, $I_h$ irreducible dimensions]{ref}
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