For carbon nanotubes, there is constructed a geometric model of polyhedral type, which allows the expressing their key structural parameters analytically, as functions of C-C bonds length and nanotube indices. In general, explicit formulas are obtained for 1D lattice constant and radius. Cylindrical coordinates of atomic sites and inter-site distances in carbon nanotubes are additionally found for achiral (zigzag and armchair) nanotubes. "Analytic" geometric model will be useful for theoretical determination of groundstate and electronic structure parameters of carbon nanotubular materials, credible analysis of corresponding experimental data, as well as purposeful designing devices based on nanotubular carbon.