Shape-selective monometallic nanocatalysts offer activity benefits based on structural sensitivity and high surface area. In bimetallic nanoalloys with well-defined shape, site-dependent metal surface segregation additionally affects the catalytic activity and stability. However, segregation on shaped alloy nanocatalysts and their atomic-scale evolution is largely unexplored. Exemplified by three octahedral PtxNi1-x alloy nanoparticle electrocatalysts with unique activity for the oxygen reduction reaction at fuel cell cathodes, we reveal an unexpected compositional segregation structure across the {111} facets using aberration-corrected scanning transmission electron microscopy and electron energy-loss spectroscopy. In contrast to theoretical predictions, the pristine PtxNi1-x nano-octahedra feature a Pt-rich frame along their edges and corners, whereas their Ni atoms are preferentially segregated in their {111} facet region. We follow their morphological and compositional evolution in electrochemical environments and correlate this with their exceptional catalytic activity. The octahedra preferentially leach in their facet centres and evolve into 'concave octahedra'. More generally, the segregation and leaching mechanisms revealed here highlight the complexity with which shape-selective nanoalloys form and evolve under reactive conditions.