Note on the asymptotic isomer count of large fullerenes

The leading term in the large- $N$ asymptotics of the isomer count of fullerenes with $N$ carbon atoms is extracted from the published enumerations for $N\le 400$ with the help of methods of series analysis. The uncovered simple $N^9$ scaling is distinct from isomer counts of most classes of chemical structures that conform to mixed exponential/power-law asymptotics. The second leading asymptotic term is found to be proportional to $N^{25/3}$ . A conjecture concerning isomer counts of the IPR fullerenes is also formulated.