Polycrystalline copper electrocatalysts have been experimentally shown to be capable of reducing CO2 into CH4 and C2H4 with relatively high selectivity, and a mechanism has recently been proposed for this reduction on the fcc(211) surface of copper, which was assumed to be the most active facet. In the current work, we use computational methods to explore the effects of the nanostructure of the copper surface and compare the effects of the fcc(111), fcc(100) and fcc(211) facets of copper on the energetics of the electroreduction of CO2. The calculations performed in this study generally show that the intermediates in CO2 reduction are most stabilized by the (211) facet, followed by the (100) facet, with the (111) surface binding the adsorbates most weakly. This leads to the prediction that the (211) facet is the most active surface among the three in producing CH4 from CO2, as well as the by-products H2 and CO. HCOOH production may be mildly enhanced on the more close-packed surfaces ((111) and (100)) as compared to the (211) facet, due to a change in mechanism from a carboxyl intermediate to a formate intermediate. The results are compared to published experimental data on these same surfaces; the predicted trends in voltage requirements are consistent between the experimental and computational data.