  Origami and crumpling are two extreme tools to shrink a 3-D shell. In the
shrink/expand process, the former is reversible due to its topological
mechanism, while the latter is irreversible because of its random-generated
creases. We observe a morphological transition between origami and crumple
states in a twisted cylindrical shell. By studying the regularity of crease
pattern, acoustic emission and energetics from experiments and simulations, we
develop a model to explain this transition from frustration of geometry that
causes breaking of rotational symmetry. In contrast to solving von
Karman-Donnell equations numerically, our model allows derivations of analytic
formula that successfully describe the origami state. When generalized to
truncated cones and polygonal cylinders, we explain why multiple and/or
reversed crumple-origami transitions can occur.
