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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.^[ref]

A zero-dimensional example is buckminsterfullerene, ${\mathrm{C}}_{60}$: a closed cage with 60 vertices, 90 edges, 12 pentagons and 20 hexagons. Euler's relation is $60-90+32=2$. Each carbon has three neighbors in a curved, approximately $s{p}^2$-bonded network; bonds are not all equivalent. Its cage diameter is of order $0.7\mathrm{nm}$.

Confinement in all directions gives discrete molecular orbitals, unlike the extended dispersion of graphene. It is an electron acceptor with characteristic electronic and vibrational spectra. Its pentagons supply the positive curvature needed to close the carbon network. A molecular solid of cages is held together predominantly by intermolecular forces, so its mechanical and electrical properties differ from those of an individual strongly bonded cage. Undoped fullerene is not a high-conductivity graphene sheet; doping, packing and charge transfer can strongly change transport.