  We posit that there exist deep and fundamental relationships between the
above seemingly very different materials. The carrier concentration-dependences
of the electronic behavior in the conducting organic charge-transfer solids and
layered cobaltates are very similar. These dependences can be explained within
a single theoretical model, - the extended Hubbard Hamiltonian with significant
nearest neighbor Coulomb repulsion. Interestingly, superconductivity in the
cobaltates seems to be restricted to bandfilling exactly or close to
one-quarter, as in the organics. We show that dynamic Jahn-Teller effects and
the resultant orbital ordering can lead to 1/4-filled band descriptions for
both superconducting spinels and fullerides, which show evidence for both
strong electron-electron and electron-phonon interactions. The orbital
orderings in antiferromagnetic lattice-expanded bcc M$_3$C$_{60}$ and the
superconductor are different in our model. Strong correlations, quarter-filled
band and lattice frustration are the common characteristics shared by these
unusual superconductors.
