In the search for boron nanotubes, the geometrical duals of carbon nanotubes, we employ the Euler−Poincare formula for a cylinder, P − C + F = 0. As may be seen in the attached figure, boron nanotubes may be imagined as arising from a correspondence between a boron atom and the center of each of the faces in a carbon nanotube.
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Gindulytė et al. (1998) studied this question.
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