We have investigated the surface structure of a curved ZnO-crystal, going from the (0001)-facet at 0° miscut to the (101¯4)-facet at a miscut of 24.8° using scanning tunneling microscopy and low energy electron diffraction. We find that the surface separates locally into (0001)-terraces and (101¯4)-facets, where the ratio between the facets depends on the miscut angle. In X-ray photoemission spectroscopy (XPS) the intensity of an O 1s component scaling with the step density of the surface is observed. No other facets were observed and the surface maintains a high degree of order over all angles. Such a curved ZnO crystal can be used for systematic studies relating the step density to the chemical reactivity using XPS to probe the curved surface at different positions.