We investigate the chemical interaction of carbon monoxide (CO) and oxygen (O2) with kink atoms on steps of platinum crystal surfaces using a specially designed Pt curved sample. We aim at describing the fundamental stages of the CO oxidation reaction, i.e., CO-covered/poisoned stage and O-covered/active stage, at the poorly known kinked Pt facets by probing CO uptake/saturation and O2 saturation, respectively. Based on the systematic analysis that the curved surface allows, and using high-resolution X-ray photoemission, a diversity of terrace and step/kink species are straightforwardly identified and accurately quantified, defining a smooth structural and chemical variation across different crystal planes. In the CO-saturated case, we observe a preferential adsorption at step edges, where the CO coverage reaches a CO molecule per step Pt atom, significantly higher than their close-packed analogous steps with straight terrace termination. For the O-saturated surface, a significantly higher O coverage is observed in kinked planes compared to the Pt(111) surface. While the strong adsorption of CO at the kinked edges points toward a higher ignition temperature of the CO oxidation at kinks as compared to terraces, the large O coverage at steps may lead to an increased reactivity of kinked surfaces during the active stage of the CO oxidation.