C1500 in the preparatory problem of IChO 2010

Problem 3 in the preparatory problem of IChO 2010 asks the buoyancy property of icosahedral buckyballs. It would be interesting but time consuming to construct all beaded models for the buckyballs with I symmetry less than 1500 carbon atoms. Right now, the largest buckyball belonging to this family I made is C320.

This problem claims that the giant buckyball are molecular balloons.
To me, the Archimedean principle of buoyancy is a macroscopic law due to the pressure course-graining over large amount of tiny collisions. Nano-particles such as C1500 have sizes less than the mean free path of the gas at 1 bar. So these nano-particles should simply follow the Boltzmann distribution, P ~ exp(-mgh/kT), based on their potential energy, mgh, at the height.