= Solution
A zero-dimensional example is \b[<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 $sp^2$-bonded network; bonds are not all equivalent. Its cage diameter is of order $0.7\ {\rm nm}$.
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.
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