Tetrahexahedral particles (similar to 10 to similar to 500 nanometers) composed of platinum (Pt), palladium, rhodium, nickel, and cobalt, as well as a library of bimetallic compositions, were synthesized on silicon wafers and on catalytic supports by a ligand-free, solid-state reaction that used trace elements [antimony (Sb), bismuth (Bi), lead, or tellurium] to stabilize high-index facets. Both simulation and experiment confirmed that this method stabilized the {210} planes. A study of the PtSb system showed that the tetrahexahedron shape resulted from the evaporative removal of Sb from the initial alloy-a shape-regulating process fundamentally different from solution-phase, ligand-dependent processes. The current density at a fixed potential for the electro-oxidation of formic acid with a commercial Pt/carbon catalyst increased by a factor of 20 after transformation with Bi into tetrahexahedral particles.