Proposed New Materials: Boron Fullerenes, Nanotubes, and Nanotori

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.