Chemical order in platinum-iridium truncated-octahedron nanoparticles as a model system was studied using coordination-dependent bond-energy variations (CBEV) and the statistical-mechanical free-energy concentration expansion method (FCEM) adapted for handling axially symmetric structures. Pt-Ir side-separated ("Quasi-Janus", QJ) configurations are found to be stabilized at low temperatures mainly due to CBEV-related preferential strengthening of Pt-surface-Ir-subsurface bonds, and the greatly reduced number of hetero-atomic bonds. In comparison, the roles of local strain (by only ∼2% atomic mismatch), short-range-order and vibrational entropy are minor. At higher temperatures, the QJ configuration is transformed into a partially disordered central-symmetric onion-like structure, and the sharp transition is accompanied by extensive pre-transition atomic exchange processes, reflected in a lambda-type heat capacity curve. The nanoparticle composition and size dependent transition temperatures, which are well below the bulk miscibility gap, furnish the first Pt-Ir nanophase diagram, which is likely to represent a distinct class of asymmetrically phase-separated nanoalloys having negligible mismatch but large preferential bond strengthening at the near-surface region.