Bcc-fcc multi-metallic nanoparticles associating a single-crystal core (Fe, FeCo alloys…) with a polycrystalline noble metal shell (Au, AuAg alloys …) are perfectly symmetrical or more irregular, even dramatically dissymmetrical, yet presenting a good crystalline organization. Here a combination of experimental analysis and theoretical symmetry analysis is proposed, in order to provide a unified description of the observed morphologies (Fe-Au and Fe-AuAg systems), whatever their symmetry, and predict some morphology variability in a population of nanoparticles. First the central role of the crystal lattice accommodation is comprehensively analyzed from the experimental Fe-AuAg system. The two possible bcc-fcc epitaxial relationships generate a core-shell interface in the shape of a truncated rhombic dodecahedron. This results in two different types of grains in the shell which are elastically accommodated between them by an equal distribution of twins and low angle grain boundaries, however at the cost of internal stresses. At the same time, a symmetry breaking results from two possible growth variants originating from the Nishiyama-Wasserman epitaxial relationships. The shell grains fit together in a nano-puzzle-like organization, resulting in a large number of possible arrangements distributed in 13 different point groups of symmetry, all of lower order than the core symmetry (highest order of cubic symmetry). If the variants are randomly distributed, the probability for the nanoparticle to be asymmetric (group 1) is 80%. The dissymmetrical development of the nanoparticles is then discussed. Extending this approach to other core shapes succeeds in predicting dissymmetrical or dramatically off-centered morphologies experimentally observed in Fe-Au nanoparticles.