Abstract
Actually existing carbon fullerenes, nanotubes, and nanotori are of interest, for reasons including their mechanical and electromagnetic properties. Because of a geometrical duality between these carbon compounds and their boron analogs, equally interesting proposed boron fullerenes, nanotubes, and nanotori are immediately suggested in a natural application of the Descartes-Euler formula, and its generalization the Euler-Poincare formula. There is a unique correspondence between the carbon and boron duals.
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