  Experiments have been performed using a spherical superconducting microwave
resonator that simulates the geometric structure of the C60 fullerene molecule.
The objective was to study with very high resolution the exceptional spectral
properties emerging from the symmetries of the icosahedral structure of the
carbon lattice. In particular, the number of zero modes has been determined to
test the predictions of the Atiyah-Singer index theorem, which relates it to
the topology of the curved carbon lattice. This is, to the best of our
knowledge, the first experimental verification of the index theorem.
