  The remarkable physical properties of buckminsterfullerene, C$_{60}$, have
attracted intense research activity since its original discovery. Total quantum
state resolved measurements of isolated C$_{60}$ molecules have been of
particularly long-standing interest. However, such observations have to date
been unsuccessful due to the difficulty in preparing cold, gas-phase C$_{60}$
in sufficiently high densities. Here we report high resolution infrared
absorption spectroscopy of C$_{60}$ in the 8.5 $\mu$m spectral region. A
combination of cryogenic buffer gas cooling and cavity-enhanced direct
frequency comb spectroscopy has enabled the observation of quantum state
resolved rovibrational transitions. Characteristic nuclear spin statistical
intensity patterns provide striking confirmation of the indistinguishability of
the sixty $^{12}$C atoms, while rovibrational fine structure encodes further
details of the molecule's rare icosahedral symmetry. These observations
establish new possibilities in the study and control of emergent complexity in
finite-sized quantum systems such as fullerenes.
