  Non-Euclidean origami is a promising technique for designing multistable
deployable structures folded from nonplanar developable surfaces. The
impossibility of flat foldability inherent to non-Euclidean origami results in
two disconnected solution branches each with the same angular deficiency but
opposite handedness. We show that these regions can be connected via "crease
stretching" wherein the creases exhibit extensibility in addition to torsional
stiffness. We further reveal that crease stretching acts as an energy storage
method capable of passive deployment and control. Specifically, we show that in
a Miura-Ori system with a single stretchable crease, this is achieved via two
unique, easy to realize, equilibrium folding pathways for a certain wide set of
parameters. In particular, we demonstrate that this connection mostly preserves
the stable states of the non-Euclidean system, while resulting a third stable
state enabled only by the interaction of crease torsion and stretching.
Finally, we show that this simplified model can be used as an efficient and
robust tool for inverse design of multistable origami based on closed-form
predictions that yield the system parameters required to attain multiple,
desired stable shapes. This facilitates the implementation of multistable
origami for applications in architecture materials, robotics, and deployable
structures.
