  Programmable shape-shifting materials can take different physical forms to
achieve multifunctionality in a dynamic and controllable manner. Although
morphing a shape from 2D to 3D via programmed inhomogeneous local deformations
has been demonstrated in various ways, the inverse problem -- programming a
sheet to take an arbitrary desired 3D shape -- is much harder yet critical to
realize specific functions. Here, we address this inverse problem in thin
liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by
precise and local control of the molecular orientation of the liquid crystal
monomers. We show how blueprints for arbitrary surface geometries as well as
local extrinsic curvatures can be generated using approximate numerical
methods. Backed by faithfully alignable and rapidly lockable LCE chemistry, we
precisely embed our designs in LCE sheets using advanced top-down
microfabrication techniques. We thus successfully produce flat sheets that,
upon thermal activation, take an arbitrary desired shape, such as a face. The
general design principles presented here for creating an arbitrary 3D shape
will allow for exploration of unmet needs in flexible electronics,
metamaterials, aerospace and medical devices, and more.
