Fig. 1: Using the Principle of Three Units (PTU) for analyzing and creating origami crease patterns.
From: Algorithmic design of origami mechanisms and tessellations
a Notational convention for angles. Dihedral angles ρ are positive for valley folds and negative for mountain folds. b Sample crease pattern graph with three interior vertices, c Corresponding crease pattern, d Unfolded and folded configuration of the crease pattern. e Folded configurations of the same crease pattern as in Fig. 1b–d folded along different kinematic paths. f Generic design procedure based on the proposed algorithmic approach. g Sample crease pattern graph with 392 interior vertices and folded configuration of the corresponding crease pattern. The graph also contains auxiliary vertices which connect boundary vertices to form boundary faces (leading to boundary vertices having two outputs). Auxiliary vertices only control the shape of the boundary faces and have no impact on the folding kinematics (for further details see Supplementary Note 1).
