Rigidity of Origami Universal Molecules
In a seminal paper from 1996 that marks the beginning of computational origami, R. Lang introduced TreeMaker, a method for designing origami crease patterns with an underlying metric tree structure. In this paper we address the foldability of paneled origamis produced by Lang’s Universal Molecule algorithm, a key component of TreeMaker.
We identify a combinatorial condition guaranteeing rigidity, resp. stability of the two extremal states relevant to Lang’s method: the initial flat, open state, resp. the folded origami base computed by Lang’s algorithm. The proofs are based on a new technique of transporting rigidity and flexibility along the edges of a paneled surface.
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