  We introduce a concise formalism to characterize nanometer-sized tori based
on carbon nanotubes and to determine their stability by combining {\em ab
initio} density functional calculations with a continuum elasticity theory
approach that requires only shape information. We find that the high strain
energy in nanotori containing only hexagonal rings is significantly reduced in
nanotori containing also other polygons. Our approach allows to determine local
curvature and link it to local strain energy, which is correlated with local
stability and chemical reactivity.
