On Rigid Origami II: Quadrilateral Creased Papers

TL;DR

This paper explores generalizations of the Miura-ori origami pattern, discovering new quadrilateral crease variations with fewer symmetries that are rigid-foldable with a single degree of freedom, expanding the understanding of rigid origami structures.

Contribution

It introduces new quadrilateral crease pattern variations related to Miura-ori, with detailed classification and methods, broadening the scope of rigid-foldable origami designs.

Findings

Discovered new variations of Miura-ori with less symmetry.

Identified quadrilateral crease patterns that are rigid-foldable with one degree of freedom.

Provided a classification and detailed explanation of these new origami variations.

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.