The possibility of interlinking buckminsterfullerene molecules via sig
ma-bonds to form novel nanostructures is considered. That is, each >>n
ode<< of such a super-structure is itself a buckyball. Particular atte
ntion is directed to regular polyhedral nanostructures as well as the
self-similar truncated icosahedral nanostructure. A systematic conside
ration of geometric constraints is presented, and an informative pertu
rbative development of the pi-MOs and their eigenspectra is made. A tr
uncated icosahedral construction yields a buckyball buckyball, and ite
ration of this construction leads toward a buckyball fractal.