There has been some interest in the alkali metal fullerides, \(\mathrm{M}_{n}
\mathrm{C}_{60}(\mathrm{s}),\) because at low temperatures, some of these
compounds become superconducting. The alkali metal fullerides are ionic
crystals comprising \(\mathrm{M}^{+}\) ions and \(\mathrm{C}_{60}^{n-}\) ions. The
value of \(n\) can be deduced from the crystal structure. If \(M_{n} C_{60}\)
consists of a cubic closest packed array of fulleride ions, with
\(\mathrm{M}^{+}\) ions occupying all the octahedral and tetrahedral holes in
the fulleride lattice, then what is the value of \(n\) and what is the empirical
formula of the fulleride?