We study the three-dimensional equilibrium shape of a shell formed by a deployed accordion-like origami, made from an elastic sheet decorated by a series of parallel creases crossed by a central longitudinal crease. Surprisingly, while the imprinted crease network does not exhibit a geodesic curvature, the emergent folded structure stemming from mechanical equilibrium yields angles at the vertices between sections of the central fold, producing an effective curvature. Both finite element analysis and manually made origamis show a robust empirical relation between the imprinted crease network’s dimensions and the apparent curvature. Moreover, the emerging structure exhibits various elastic deformations that induce three distinct morphogenesis types, from bent faces to complete faceting to structural buckling. We characterize the corresponding kinematics of crease network deformations and determine their phase diagram. Taking advantage of the frustration caused by the competition between crease stiffness and kinematics of crease network deformations, we provide a novel tool for designing curved origami structures constrained by strong geometrical properties.