  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 structure is characterized by an effective curvature
produced by the deformed central fold. Moreover, both finite element analysis
and manually made mylar origamis show a robust empirical relation between the
imprinted crease network's dimensions and the apparent curvature. A detailed
examination of this geometrical relation shows the existence of three typical
elastic deformations, which in turn induce three distinct types of
morphogenesis. 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.
