Well-faceted polyhedral Rh nanocrystals, epitaxially grown on NaCl (001) and supported by amorphous alumina, were selected to study the effect of oxidation and reduction on particle microstructure and on catalytic properties. The crystal habit, surface structure, and surface composition of the crystallites were determined by high-resolution electron microscopy assisted by digital image processing and contrast simulation, by weak-beam dark-field imaging, and by selected area electron diffraction. Their catalytic performance in the hydrogenolysis of alkanes was tested by microreactor kinetics. In the as-prepared state most Rh crystallites had smooth, low-Miller-index bounding faces and exhibited a half-octahedral or half-tetrahedral shape. Because of their regular habit these particles represent a well-defined initial state in a study of activation-induced morphology changes. After oxidation at 575 K a thin surface oxide was evident, whereas oxidation at 725 K led to the oriented overgrowth of hexagonal alpha-Rh2O3 on Rh. Oxidation at 725 K followed by low-temperature reduction at 525 K produced Rh particles with disordered surfaces, e.g., polycrystalline Rh particles or sandwich structures of Rh and Rh2O3 However, when oxidation at 725 K was followed by high-temperature reduction at 725 K, the low-Miller-index facets were reestablished. High turnover frequencies were observed on catalysts containing mainly Rh particles with disordered ("rough") surfaces, whereas smooth close-packed facets dominated in less active catalysts. The results confirm that high-index faces (low-coordinated sites) are preferred for hydrogenolysis.