The energy approximation in eq. 1 accounts for and quantifies contributions from metal atoms in different co-ordination environments. Understanding the transition from the TO to the ATO shape is thus possible by analyzing the varying distribution of coordination numbers for the two metals (see Table ). The two shapes have the exact same average coordination number. However, the ATO has more 12-coordinated bulk-like atoms, compensated with an average lower coordination number of surface sites. This distortion in the distribution of coordination numbers is particularly relevant in terms of stability when surface and bulk-like sites are occupied by Au and Pt atoms, respectively.