The remarkable synthetically tunable structural, electronic, and optical properties of gold nanocrystals have attracted increasing interest and enabled multidisciplinary applications. Over the past decades, nearly all the possible fundamental shapes of faceted Au nanocrystals have been synthesized, except for only one missing-the trapezohedron enclosed by {hkk} facets. In this report, the unprecedented synthesis of trapezohedral Au nanocrystals with {311} crystal facets was realized. Dimethyl sulfoxide (DMSO) was discovered as a solvent for shaping Au nanocrystals with {311} crystal facets for the first time. Mechanistic studies, together with previous DFT and STM studies, attribute the unique role of DMSO to its ambidentate nature, where both sulfur and oxygen of DMSO can coordinate to gold surface, endowing its unique role in stabilizing high-index {311} facets through a "two center bonding" mode. The DMSO-based synthesis provides a new synthetic tool toward the synthesis of a series of unreported Au nanocrystals with new structures. In particular, a new type of gold bipyramids, the octagonal bipyramids, was first synthesized with additional plasmonic tunability while simultaneously retaining their {311} facets. The application of these new Au nanocrystals in surface-enhanced Raman scattering spectroscopy was investigated, and their shape-dependent performances were demonstrated. These results highlight the tremendous potential of using ambidentate molecules as shape- and surface-directing agents for metal nanocrystals and offer the promise of enabling new synthetic tools toward atomically precise control of surface structures of metal nanocrystals.