Abstract
The Descartes−Euler formula, P + F = C + 2, which is known to apply to single cage carbon and boron fullerenes, is shown here to apply to multicage fullerenes as well. Every carbon multicage fullerene has a corresponding boron multicage geometrical dual, of identical symmetry, as for example in the case of C47 and B30H302-, shown here. The proposed boron multicage fullerenes are studied with molecular orbital calculations to establish their energetic stability, bond lengths, and ionic charge state.
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