A geometric constraint, the head-to-tail exclusion rule, may be the basis for the isolated-pentagon rule in fullerenes with more than 60 vertices.

Carbon atoms self-assemble into the famous soccer-ball shaped Buckminsterfullerene (C(60)), the smallest fullerene cage that obeys the isolated-pentagon rule (IPR). Carbon atoms self-assemble into larger (n > 60 vertices) empty cages as well-but only the few that obey the IPR-and at least 1 small fullerene (n 60, the head-to-tail exclusion rule permits only (and all) fullerene cages and nanotubes that obey the IPR. We therefore suggest that self-assembly that obeys the IPR may be explained by the head-to-tail exclusion rule, a geometric constraint.