Abstract
A new, general type of two-dimensional foldable structures is presented, which extends and generalises the standard trellis-type foldable structure consisting of two sets of parallel straight rods connected by hinges. It is shown that any structure consisting of rigid, multi-angulated rods, i.e., straight rods with kinks at the hinge positions, can be folded if the rods form a tessellation of parallelograms. This discovery is exploited to investigate the structural layouts of flat and curved structures which can be folded along their perimeter.
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