In this study, we have successfully developed a facile method for the high-yield fabrication of Au-Pd core shell heterostructures with an unusual tetrahexahedral (THH) morphology using Au nanocubes as the structure-directing cores. The lattice orientations of the Au nanocubes match those of the Pd shells. Structural analysis establishes that the THH nanocrystals are bounded by high-index {73 0} facets. A substantial lattice mismatch between Au and Pd, oxidative etching in the presence of chloride and oxygen, the use of cetyltrimethylammonium chloride (CTAC) surfactant, and the reaction temperature (30-60 degrees C) were identified to be key factors facilitating the formation of the THH core shell nanocrystals. Intermediate products have also been examined to follow the growth process. By selecting cubic gold cores with sizes of 30-70 nm and varying the volume of the gold core solution used, THH Au Pd core shell nanocrystals with continuously adjustable sizes from 56 to 124 nm can be readily obtained. Their UV vis spectra display progressive red-shifted bands. Interestingly, novel concave octahedral and octahedral Au Pd core shell nanocrystals can be prepared by lowering the reaction temperature and prolonging the reaction time. The concave octahedra show depressions on all the {1 1 1} faces. Electrocatalytic activity of the three Au Pd core shell structures for the oxidation of ethanol has been investigated. The THH nanocrystals with entirely high-index {7 30} facets were found to exhibit the best electrocatalytic activity. These size-tunable THH Au-Pd core-shell nanocrystals may be valuable for catalyzing other organic reactions.