Nematic elastomers dramatically change their shape in response to diverse
stimuli including light and heat. In this paper, we provide a systematic
framework for the design of complex three dimensional shapes through the
actuation of heterogeneously patterned nematic elastomer sheets. These sheets
are composed of \textit{nonisometric origami} building blocks which, when
appropriately linked together, can actuate into a diverse array of three
dimensional faceted shapes. We demonstrate both theoretically and
experimentally that: 1) the nonisometric origami building blocks actuate in the
predicted manner, 2) the integration of multiple building blocks leads to
complex multi-stable, yet predictable, shapes, 3) we can bias the actuation
experimentally to obtain a desired complex shape amongst the multi-stable
shapes. We then show that this experimentally realized functionality enables a
rich possible design landscape for actuation using nematic elastomers. We
highlight this landscape through theoretical examples, which utilize large
arrays of these building blocks to realize a desired three dimensional origami
shape. In combination, these results amount to an engineering design principle,
which we hope will provide a template for the application of nematic elastomers
to emerging technologies
