  Kirigami involves cutting a flat, thin sheet that allows it to morph from a
closed, compact configuration into an open deployed structure via coordinated
rotations of the internal tiles. By recognizing and generalizing the geometric
constraints that enable this art form, we propose a design framework for
compact reconfigurable kirigami patterns, which can morph from a closed and
compact configuration into a deployed state conforming to any prescribed target
shape, and subsequently be contracted into a different closed and compact
configuration. We further establish a condition for producing kirigami patterns
which are reconfigurable and rigid deployable allowing us to connect the
compact states via a zero-energy family of deployed states. All together, our
inverse design framework lays out a new path for the creation of shape-morphing
material structures.
