Silver nanoparticles with a single (111) twin were selectively nucleated and grown for the first time to produce right bipyramids 75-150 nm in edge length. Key to the production of single twinned seeds was the addition of NaBr to a polyol synthesis in which AgNO3 is reduced by ethylene glycol in the presence of poly(vinyl pyrrolidone). Examination of nanoparticles at different stages of the reaction with electron microscopy revealed that the spherical, single twinned seeds grew to become right bipyramids through enlargement of their (100) facets. The UV-vis-NIR spectrum exhibited by right bipyramids is distinct from that of any other silver nanostructure, and their sharp corners make these new nanoparticles especially promising for enhancement of Raman scattering.