The systematic construction of heterogeneous nanoparticles composed of two distinct metal domains (Au and Pt) and exhibiting a broad range of morphologically defined shapes is reported. It is demonstrated that careful Au overgrowth on Pt nanocrystal seeds with shapes mainly corresponding to cubeoctahedra, octahedra and octapods can lead to heterometallic systems whose intrinsic structures result from specific epitaxial relationships such as {111} + {111}, {200} + {200} and {220} + {220}. Comprehensive analysis shows also that nanoparticles grown from octahedral seeds can be seen as comprising of four Au tetrahedral subunits and one Pt octahedral unit in a cyclic arrangement that is similar to the corresponding one in decahedral gold nanoparticles. However, in the present case, the multi-component system is characterized by a broken five-fold rotational symmetry about the [011] axis. This set of bimetallic dimers could provide new platforms for fuel cell catalysts and plasmonic devices.