  We investigate the chirality dependence of physical properties of nanotubes
which are wrapped by the planar hexagonal lattice including graphite and boron
nitride sheet, and reveal its symmetry origin. The observables under
consideration are of scalar, vector and tensor types. These exact chirality
dependence obtained are useful to verify the experimental and numerical results
and propose accurate empirical formulas. Some important features of physical
quantities can also be extracted by only considering the symmetry restrictions
without complicated calculations.
