Fullerene C50: Sphericity takes over, not strain

It is commonly accepted that the most stable fullerene geometry among all possible structures built from hexagons and 12 pentagons is that with minimum strain. This implies that the most stable structure corresponds to the minimum number of adjacent pentagons. Here, we report that the fullerene C50 and some of its endohedral derivatives do not follow this rule. We show that an additional 'sphericity rule' is necessary for magic number fullerenes when nearly spherical shapes can be adopted by increasing the number of adjacent pentagons. The same rule explains why exohedral derivatives such as C50Cln or C50Hn do not follow this behavior.