On Rigid Origami II: Quadrilateral Creased Papers

Abstract

Miura-ori is well-known for its capability of flatly folding a sheet of paper through a tessellated crease pattern made of repeating parallelograms. Many potential applications have been based on the Miura-ori and its primary variations. Here we are considering how to generalize the Miura-ori: what is the collection of rigid-foldable creased papers with a similar quadrilateral crease pattern as the Miura-ori? This paper reports some progress. We find some new variations of Miura-ori with less symmetry than the known rigid-foldable quadrilateral meshes. They are not necessarily developable or flat-foldable, and still only have single degree of freedom in their rigid folding motion. This article presents a classification of the new variations we discovered and explains the methods in detail.

arXiv commentMain text 24 pages, 9 figures, 2 tables, Supplementary Material 13 pages, 2 figures; submitted to the Proceedings of the Royal Society A, in minor revision

References in corpus (1)

• On Rigid Origami I: Piecewise-planar Paper with Straight-line Creases

Cited by in corpus (8)

• The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
• Flexible Kokotsakis Meshes with Skew Faces: Generalization of the Orthodiagonal Involutive Type
• Area preserving Combescure transformations
• Lorentz transformation for the kinematics of degree-4 rigid origami vertices and compatibility of rigid-foldable polygons
• Quasi-symmetric nets: A constructive approach to the equimodular elliptic type of Kokotsakis polyhedra
• Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean
• Explosive rigidity percolation in origami
• Unlocking Euclidean Problems with Isotropic Initialization