A 15-dimensional analytical form for the potential energy and dipole moment surfaces of the SF6 molecule in the ground electronic state is obtained using ab initio methods. In order to calculate the equilibrium S-F distance, we applied the coupled cluster CCSD(T) method and several versions of the correlation-consistent basis sets from valence triple-zeta (VTZ) and augmented valence triple-zeta (AVTZ) to core-valence quadruple-zeta (CVQZ) with Douglas-Kroll (DK) relativistic corrections that provided good agreement with an empirical equilibrium value. Ab initio electronic energies on 15D grids of nuclear geometries are computed using the CCSD(T) method with VTZ and CVQZ-DK basis sets. The analytical representation of the potential energy surface is determined through an expansion in symmetry-adapted products of nonlinear coordinates up to the 5th order. The influence of additional redundant coordinates on the quality of the fit was investigated. Parameters of full-dimensional dipole moment surfaces are determined up to the 4th order expansion in normal mode coordinates. For validation of ab initio results, the fundamental vibration frequencies and absorption cross sections of the principal sulfur hexafluoride isotopologue are calculated, giving good agreement with cold (180 K) and room temperature (296 K) experimental spectra. Absorption cross sections calculated from our preliminary line list agree much better with these observations than the simulations using SF6 line-by-line lists constructed from effective models included in currently available spectroscopic databases.