We investigated various two-dimensional (2D) and three-dimensional (3D) structures of H+(H2O)(8), using density functional theory (DFT), Moller-Plesset second-order perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations (CCSD(T)). The 3D structure is more stable than the 2D structure at all levels of theory on the Born-Oppenheimer surface. With the zero-point energy (ZPE) correction, the predicted structure varies depending on the level of theory. The DFT employing Becke's three parameters with Lee-Yang-Parr functionals (B3LYP) favors the 2D structure. At the complete basis set (CBS) limit, the MP2 calculation favors the 3D structure by 0.29 kcal/mol, and the CCSD(T) calculation favors the 3D structure by 0.27 kcal/mol. It is thus expected that both 2D and 3D structures are nearly isoenergetic near 0 K. At 100 K, all the calculations show that the 2D structure is much more stable in free binding energy than the 3D structure. The DFT and MP2 vibrational spectra of the 2D structure are consistent with the experimental spectra. First-principles Car-Parrinello molecular dynamics (CPMD) simulations show that the 2D Zundel-type vibrational spectra are in good agreement with the experiment.