Fast scanning calorimetry and single-crystal synchrotron diffraction have been used to explore the regimes of stability and metastability of the curved bucky-bowl corannulene. Unlike their flat counterparts, cooling rates above 500 K/s from the melt are effective at preventing crystallisation, leading to a glassy state below ambient conditions. Upon heating from the glass, we observe a series of three sharp thermal events at ca. 380, 430, and 500 K associated with hitherto unknown polymorphs of this carbon-based solid. The single-crystal diffraction data provide a framework to understand this rich phenomenology in terms of the activation of well-defined molecular rotations that increase the occupancy of interstitial sites and trigger a sharp decrease in density near the observed glass-transition temperature. These changes are also accompanied by abnormally high atomic displacement parameters as the temperature where the first (and strongest) cold-crystallisation event is observed. The diffraction data also provide strong evidence that solid CA ought to be regarded as two distinctly different materials below and above the aforementioned glass-transition temperature. Altogether, our findings bring to the fore the unanticipated complexity underpinning the structure and thermodynamic response of solid corannulene, the simplest geodesic polyarene.