Ab initio coupled and uncoupled Hartree-Fock polarizabilities are computed for increasingly large oligothiophenes using the 3-21G, 6-31G**, 6-311G**, and the Sadlej medium-size polarized atomic basis sets. The comparison with experimental values highlights the large sensitivity of the measured polarizabilities with respect to working conditions. By extrapolating to the infinite chain limit the polarizability values of increasingly large oligomers, we compute the asymptotic polarizabilities per thiophene ring. The transversal, perpendicular, and longitudinal asymptotic coupled Hartree-Fock polarizabilities per thiophene ring are, using the 3-21G (631G**) atomic basis set, 49.7 (52.5), 15.2 (20.6), and 184.1 (190.0) a.u., respectively. Polythiophene is more polarizable than polydiacetylene, polyyne, and polysilane but less polarizable than polyacetylene which, in contrast to polythiophene, is much more difficult to process. Using a procedure which relates the polarizability and the topology of the one-particle states, the major contribution to the polarizability is attributed to pi-symmetry crystalline orbitals located at the top of the valence bands, which look like an alternation of segments of the highest occupied crystalline orbitals of the all-trans and trans-cisoid polyacetylene. However, a sizeable a contribution domes from sigma-conjugated segments formed by the sulfur atoms and their two adjacent carbon atoms.