We have calculated surface energies and surface magnetic order of various low-indexed surfaces of monoatomic Fe, Co, and Pt, and binary, ordered FePt, CoPt, and MnPt using density-functional theory. Our results for the binary systems indicate that elemental, Pt-covered surfaces are preferred over Fe and Co covered and mixed surfaces of the same orientation. The lowest energy orientation for mixed surfaces is the highly coordinated (111) surface. We find Pt-covered (111) surfaces, which can be realized in the L11 structure only, to be lower in energy by about 400 meV/atom compared to the mixed L10 (111) surface. We conclude that in small nanoparticles this low surface energy can stabilize the L11 structure, which is suppressed in bulk alloys. From the interplay of surface and bulk energies, equilibrium shapes of single-crystalline ordered nanoparticles and crossover sizes between the different orderings can be estimated.