We next address the interplay between shape and composition for particle sizes that cannot form the symmetric and very stable truncated octahedron shape typical of e.g. 79-, 140-, 201-atom particles. Although these magic numbers form particularly stable particles, experimentally prepared metal NPs typically exhibit a rather wide particle size distribution . To generalize the interplay between size and shape to non-magic number particle sizes, we have repeated the minimum-energy hull linescan optimization (fitting eq. 1 to EMT energies) for (Au n Pt m-n ) for m = 135, 145, and 150. The resulting ensembles of minimum-energy hulls for each of these particle sizes are shown in Figs. S8 to S11, and the two most relevant structures for each size are shown in Fig. .