How many buckyballs are there with 2n carbon atoms? Equivalently, how many triangulations of the sphere are there with 2n triangles, so that each vertex has valence 6 or less? I will describe joint work with Peter Smillie which shows that if one counts with the correct weight, the answer is exactly 809/2612138803200 * sigma_9(n) where sigma_9(n) is the sum of the ninth powers of the divisors of n.