It is interesting to examine facet-dependent electrical properties of single Cu2O crystals, because such study greatly advances our understanding of various facet effects exhibited by semiconductors. We show a Cu2O octahedron is highly conductive, a cube is moderately conductive, and a rhombic dodecahedron is nonconductive. The conductivity differences are ascribed to the presence of a thin surface layer having different degrees of band bending. When electrical connection was made on two different facets of a rhombicuboctahedron, a diode-like response was obtained, demonstrating the potential of using single polyhedral nanocrystals as functional electronic components. Density of state (DOS) plots for three layers of Cu2O (111), (100), and (110) planes show respective metallic, semimetal, and semiconducting band structures. By examining DOS plots for varying number of planes, the surface layer thicknesses responsible for the facet-dependent electrical properties of Cu2O crystals have been determined to be below 1.5 nm for these facets.