Fig. 4: Fabricated Arc-Miura origami.
A Fabricated tessellation with primitive lattice vectors ℓ1,2. B Primitive cell vertices labeled a, b, c, and d and faces labeled \({{\mathcal{A}}},{{\mathcal{B}}},{{\mathcal{C}}}\), and \({{\mathcal{D}}}\). C Sector angles labeled α and \({\alpha }^{{\prime} }\equiv \pi -\alpha\) and dihedral angles labeled γ, ψ, and ψ″ ≡ 2π − ψ. D Compatibility diagram with amplitudes \({{{\mathcal{V}}}}^{a},{{{\mathcal{V}}}}^{b},{{{\mathcal{V}}}}^{c}\), and \({{{\mathcal{V}}}}^{d}\) on the corresponding vertices and colors indicating the coupling coefficients ζ/q, − ξ/s, and  + ξ/p. E Edge lengths labeled p, q, and s. F View of folded specimen with height h, exterior radius Re, and interior radius Ri with the mountain valley assignment of the folded creases indicated. G Radius as a function of height comparing one set of experimental measurements on one sample with theoretical predictions. Black dashed line indicates flattened state. H Excitation of the non-rigid isometry. Scale bar is 30 mm in both panels (F, H).
