Well-defined surfaces of Pt have been extensively studied for various catalytic processes. However, industrial catalysts are mostly composed of fine particles (e.g., nanocrystals), due to the desire for a high surface to volume ratio. Therefore, it is very important to explore and understand the catalytic processes both at nanoscale and on extended surfaces. In this report, a general synthetic method is described to prepare Pt nanocrystals with various morphologies. The synthesized Pt nanocrystals are further purified by exploiting the "self-cleaning" effect which results from the "colloidal recrystallization" of Pt supercrystals. The resulting high-purity nanocrystals enable the direct comparison of the reactivity of the {111} and {100} facets for important catalytic reactions. With these high-purity Pt nanocrystals, we have made several observations: Pt octahedra show higher poisoning tolerance in the electrooxidation of formic acid than Pt cubes; the oxidation of CO on Pt nanocrystals is structure insensitive when the partial pressure ratio p(O2)/p(CO) is close to or less than 0.5, while it is structure sensitive in the O(2)-rich environment; Pt octahedra have a lower activation energy than Pt cubes when catalyzing the electron transfer reaction between hexacyanoferrate (III) and thiosulfate ions. Through electrocatalysis, gas-phase-catalysis of CO oxidation, and a liquid-phase-catalysis of electron transfer reaction, we demonstrate that high quality Pt nanocrystals which have {111} and {100} facets selectively expose are ideal model materials to study catalysis at nanoscale.