Developing syntheses of more sophisticated nanostructures comprising late transition metals broadens the tools to rationally design suitable heterogeneous catalysts for chemical transformations. Herein, we report a synthesis of Pd-Rh nanoboxes by controlling the migration of metals in a core-shell nanoparticle. The Pd-Rh nanobox structure is a grid-like arrangement of two distinct metal phases, and the surfaces of these boxes are {100} dominant Pd and Rh. The catalytic behaviors of the particles were examined in electrochemistry to investigate strain effects arising from this structure. It was found that the trends in activity of model fuel cell reactions cannot be explained solely by the surface composition. The lattice strain emerging from the nanoscale separation of metal phases at the surface also plays an important role.