  Designing flat sheets that can be made to deform into 3D shapes is an area of
intense research with applications in micromachines, soft robotics, and medical
implants. Thus far, such sheets could only be made to adopt a single family of
shapes. Here, we show that through anisotropic deformation applied
inhomogenously throughout a sheet, it is possible to design a single sheet that
can deform into multiple surface geometries upon different actuations. The key
to our approach is development of an analytical method for solving this
multi-valued inverse problem. Such sheets open the door to fabricating machines
that can perform complex tasks through cyclic transitions between multiple
shapes. As a proof of concept we design a simple swimmer capable of moving
through a fluid at low Reynolds numbers.
