In terms of intermolecular bonding present in buckminsterfullerene, in the solid is Van Der Waals dispersion forces. This directly links with the fact that it has a lower boiling point than the other two common allotropes of carbon, diamond and graphite, because they would have a lot more covalent bonding going on (Chemguide, n.d.).
Then just to finish off the observations about whats going on inside this molecule, theres also some hybridization going on. Following the VSEPR theory, each carbon has sp^2 hybridization with the remaining p-orbital available for bonding with one of the adjacent carbon atoms. So overall, each carbon forms three bonds with its sp^2 hybrid orbital and one bond with the remaining p-orbital (Chemical Bonding, n.d.).