We report highly facet-dependent electrical properties of Cu2O nanocubes and octahedra and significant enhancement of gold nanocrystal cores to the electrical conductivity of Au Cu2O core shell octahedra. Cu2O nano following our reported facile procedures at room temperature. Two oxide-free tungsten cubes and octahedra and Au Cu2O core shell cubes and octahedra were synthesized by probes attached to a nanomanipulator installed inside a scanning electron microscope made contacts to a single Cu2O nanocrystal for the I V measurements. Pristine Cu2O octahedra bounded by 11111 facets are 1100 times more conductive than pristine Cu2O cubes enclosed by {100} faces, which are barely conductive. Core shell cubes are only slightly more conductive than pristine cubes. A 10000-fold increase in conductivity over a cube has been recorded for an octahedron. Remarkably, core shell octahedra are far more conductive than pristine octahedra. The same facet-dependent electrical behavior can still be observed on a single nanocrystal exposing both {111} and {100} facets. This new fundamental property may be observable in other semiconductor nanocrystals. We also have shown that both core shell cubes and octahedra outperform pristine cubes and octahedra in the photodegradation of methyl orange. Efficient photoinduced charge separation is attributed to this enhanced photocatalytic activity. Interestingly, facet-selective etching occurred over the {100} corners of some octahedra and core shell octahedra during photocatalysis. The successful preparation of Au Cu2O core shell heterostructures with precise shape control has offered opportunities to discover new and exciting physical and chemical properties of nanocrystals.