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Quadrilatera creased paper: Origami fold pattern

Reference [2] is:

Tachi T. 2009 Generalization of rigid-foldable quadrilateral-mesh origami. J. Int. Assoc. Shell Spatial Struct. 50, 173–179.

FROM:

Zeyuan He and Simon D. Guest (Civil Engineering Building, Department of Engineering, 7a JJ Thomson Ave, Cambridge CB3 0FA, USA),

“On rigid origami II: quadrilateral creased papers”, Proceedings of the Royal Society Series A, Vol. 476, No. 2237, Article ID:20200020, 1 May 2020, https://doi.org/10.1098/rspa.2020.0020

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.

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