The atomic structure and chemical ordering of Ni-Pt nanoalloys of different sizes and shapes are studied by numerical simulations using Monte Carlo methods and a realistic interatomic potential. The bulk Ni-Pt ordering tendency remains in the fcc nanoparticles but we show some chemical ordering frustrations linked to surface reconstructions depending on the cluster size and shape. A reversed temperature dependence of Pt surface segregation is also established. In the particular case of fivefold symmetry as in icosahedra, ordering is observed in the core and on the facets at low temperatures with a segregation of the smaller element (Ni) in the core because of atomic strain. We show that the icosahedral shape favors Pt surface segregation in comparison with octahedral and truncated octahedral structures.