We demonstrate photocatalytic reduction of methylene blue in the infrared region, using PbSe/CdSe/CdS core/shell/shell heterostructure nanocrystals (HNCs) with type II or quasi-type II band offsets. Varying deposition rates of the CdS shell result in nanocrystals of diverse morphologies ranging from spheres to pyramids to tetrapods. The faceted shapes enable the selective growth of Au tips, which help increase photocatalytic activity since the Au tips serve as an electron sink. Comparative studies reveal that the photocatalytic activity appears to correlate with the integral overlap of electron and hole wave functions. Tetrapod-shaped HNCs with Au tips show considerably higher photocatalytic activity for the reduction of methylene blue than sphere or pyramid-shaped HNCs of equivalent composition arrangement.