Bimetallic FePt nanoparticles with L1 ₀ structure are attracting a lot of attention due to their high magnetocrystalline anisotropy and high coercivity what makes them potential material for storage of ultra-high density magnetic data. FePt nanoclusters are considered also as nanocatalysts for growth of carbon nanotubes of different chiralities. Using the DFT-LCAO CRYSTAL14 code, we have performed large-scale spin-polarized calculations on 19 different polyhedral structures of FePt nanoparticles in order to estimate which icosahedral or hcp-structured morphology is the energetically more preferable. Surface energy calculations of all aforementioned nanoparticles indicate that the global minimum corresponds to the nanocluster possessing the icosahedron "onion-like" structure and Fe₄₃Pt₁₀₄ morphology where the outer layer consists of Pt atoms. The presence of the Pt-enriched layer around FePt core explains high oxidation resistance and environmental stability, both observed experimentally.