Fig. 3: Arc-Morph origami.
A Perspective view of an example configuration with N1 = 4 cells in the azimuthal direction and N2 = 4 cells in the axial direction. B Primitive cell with vertices labeled a, b, c, and d, faces labeled \({{\mathcal{A}}},{{\mathcal{B}}},{{\mathcal{C}}}\), and \({{\mathcal{D}}}\), and edge lengths labeled p = 1, q = 0.7, sα, and sβ. C Sector angles labeled \(\alpha=1.1,{\alpha }^{{\prime} }\equiv \pi -\alpha,\beta=2.1,{\beta }^{{\prime} }\equiv \pi -\beta\) and dihedral angles labeled γ, ψ, ψ″ ≡ 2π − ψ, and θ, θ″ ≡ 2π − θ. D Compatibility diagram for vertex amplitudes with edges representing the coupling coefficients based on the folding coefficients ζ, ξ, and χ. E Nonlinear evolution of the height and radius of the crease pattern shown in panel A along the rigid folding mode, with the flat folded state shown in (F), maximal height state shown in (G), and closed state shown in (H). F–H Front and top-down views of states labeled in (E, I). I Linear response along the configuration manifold as a function of the dihedral angle, γ, quantified by the pitch p induced by the non-rigid mode and the ratio dh/dR of the rigid mode. The curve is shaded towards σ2 = 0 for illustration purposes.
