<p>The formalism of line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry has been applied for symmetry analysis of single-walled titania nanotubes (SW TiO2 NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of anatase structure. Either six- or twelve-layer (101) slabs have been cut from TiO2 crystal in a stable anatase phase. After structural optimization, the latter keeps the centered rectangular symmetry of initial slab slightly compressed along a direction coincided with large sides of elemental rectangles. We have considered two sets of SW TiO2 NTs with optimized six- and twelve-layer structures, which possess chiralities (&minus;n, n) and (n, n) of anatase nanotubes. To analyze the structural and electronic properties of titania slabs and nanotubes, we have performed their ab initio LCAO calculations, using the hybrid Hartree-Fock/Kohn-Sham exchange-correlation functional PBE0. The band gaps (∆&epsilon;gap) and strain energies (Estrain) of six-layer nanotubes have been computed and analyzed as functions of NT diameter (DNT). As to models of 12-layer SW TiO2 NTs of both chiralities, their optimization results in structural exfoliation, i.e., the multi-walled structure should be rather formed in nanotubes with such a number of atomic layers.</p>