We combine first-principles atomistic thermodynamics with a Wulff-Kaichew construction to determine the equilibrium shape of Ag particles supported on alpha-Al2O3(0001) under gas-phase conditions representative for ethylene epoxidation. The formation of three-dimensional truncated octahedra is predicted for both the Al-terminated (AlO3Al-R) and the fully hydroxylated O-terminated (H3O3Al-R) alumina surface, albeit with largely different contact angles. Overall, this is fully consistent with the common description of hemispherical Ag microcrystals on this support, but at variance with the cubic Ag nanoparticles reported recently by Christopher and Linic (2008). This result suggests the latter particles to be stabilized kinetically. We establish a framework from which strategies to thermodynamically stabilize cubic particles can be explored. The Wulff-Kaichew construction is proposed to provide a straightforward criterion that may be used as a suitable descriptor in the computational screening of surface additives that would stabilize the arguably highly selective Ag(100) facets. (c) 2014 Elsevier Inc. All rights reserved.