Controlling the shape and thus facets of metal nanocrystals is an effective way to enhance their performance in catalytic reactions. While Pd nanocrystals with a myriad of shapes have been successfully prepared with good uniformity and in high yield, Pd right bipyramids (RBPs) that have a singly twinned structure have been elusive. We report a facile route based on polyol reduction for the synthesis of Pd RBPs with purity >90% and sizes controlled in the range 5-15 nm. The success of our synthesis relies on the use of iodide ions to manipulate the strength of an oxidative etchant and selectively cap the Pd{100} facets. The as-prepared RBPs could serve as seeds to generate a set of Pd nanocrystals with novel shapes and structures. The RBPs also exhibited enhanced catalytic activity toward formic acid oxidation, with a current density 2.5 and 7.1 times higher than those of the single-crystal Pd nanocubes (which were also mainly covered by {100} facets) and commercial Pd black, respectively.