We investigated five lowest energy structures of the water hexamer (ring, book, bag, cage, and prism) using extensive ab initio calculations. High levels of theory using various basis sets were employed. On the basis of Moller-Plesset second order perturbation (MP2) calculations using a large basis set [9s6p4d2 f1g/6s4p2d] + diffuse(2sp/s), the lowest energy structure with zero point energy (ZPE) correction is the cage conformer, followed by the book (within 0.1 kcal/mol) and the prism (within 0.2 kcal/mol). The spectra of the five conformers have been investigated. The predicted rotational constants and dipole moments of the cage conformer are in good agreement with the experiment [Liu et nl., Nature 381, 501 (1996)] as compared to other structures. This proves that the experiment surely found the cage structure, which was first reported by one of the authors [Kim et nl., Chem. Phys. Lett. 131, 451 (1986)]. However, the five structures would still be nearly isoenergetic within 0.7 kcal/mol at 0 K. Above similar to 40 K, the free energy of the book is slightly lower than the cage, which might imply that the book structure would be detected. Upon deuteration, the cage structure is the lowest energy conformer, followed by two competing structures of the book and prism whose energies are only 0.2 kcal/mol higher at 0 K; above similar to 55 K the book would be more populated than the cage.