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We present a nuclear magnetic resonance (NMR) study of ${\mathrm{Na}}_{2}{\mathrm{C}}_{60}$ and ${\mathrm{K}}_{4}{\mathrm{C}}_{60},$ two compounds that are related by electron-hole symmetry in the ${\mathrm{C}}_{60}$ triply degenerate conduction band. In both systems, it is known that NMR spin-lattice relaxation rate ${(1/T}_{1})$ measurements detect a gap in the electronic structure, most likely related …