The shapes of noble metal nanocrystals (NCs) are usually defined by polyhedra that are enclosed by {111} and {100} facets, such as cubes, tetrahedra, and octahedra. Platinum NCs of unusual tetrahexahedral (THH) shape were prepared at high yield by an electrochemical treatment of Pt nanospheres supported on glassy carbon by a square-wave potential. The single-crystal THH NC is enclosed by 24 high-index facets such as {730}, {210}, and/or {520} surfaces that have a large density of atomic steps and dangling bonds. These high-energy surfaces are stable thermally (to 800 degrees C) and chemically and exhibit much enhanced (up to 400%) catalytic activity for equivalent Pt surface areas for electro-oxidation of small organic fuels such as formic acid and ethanol.