Ab initio and density functional calculations show that the equilibrium structure of hexamethyltungsten is a distorted trigonal prism of C-3 symmetry (with local C-3v symmetry for the WC6 skeleton). A regular prismatic D-3 structure (with D-3h skeleton) is found to be ca. 20 kT mol(-1) higher in energy at correlated levels of theory. It is a transition state connecting two C-3 minima. These results extend a recent gas-phase electron diffraction study which favored a regular prismatic structure but could not rule out a distortion to C-3v The failure of a previous theoretical study to locate the distorted minimum is due to the neglect of electron correlation and to some other restrictions during the structure optimizations. Correlation is important, e.g. for the description of hyperconjugative "agostic" C-H-->W interactions which are found to be pronounced in W(CH3)6 Structures optimized with gradient-corrected or hybrid density functionals, or at the MP2 level, describe these interactions well. The observed single-line C-13 and H-1 NMR spectra are explained by dynamic motions due to the low D-3 inversion and methyl rotation barriers. C-13 chemical shifts calculated using density functional theory differ by ca. 18 ppm between the two nonequivalent sets of methyl groups in the distorted trigonal prismatic structure. Low-temperature NMR experiments could be useful to confirm this value and thus the distortion. Harmonic vibrational frequency analyses are consistent with experimental results and have been used to characterize stationary points on the potential energy surface. Differences between the structural preferences of W(CH3)(6) and WH6 are investigated via detailed bonding analyses.