Our recent work on Germanium Fluoride nanocages was accepted by the Journal of the American Chemical Society. In this work, we studied with DFT a series of high-symmetry molecules with Formula GenFn, where n is between six and sixty. The molecules we studied show optical transparency or semi-transparency, electron delocalization, LUMO energies below -4 eV, and gaps in the range 1.6-3.2 eV. Although the formation energies are high, the fullerene-like systems have isomers with lower ground-state energies, where some Fluorine atoms are located inside the cages. So the fullerene below could undergo a transformation with F atoms preferring to be inside; but the barrier for such a transition should be very high.