2018/04/17 by Zeyuan He, Simon D. Guest, He, Zeyuan +1 · 6 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Metric Geometry (math.MG) #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft #math.MG
paper · pdf · doi:10.48550/arxiv.1804.06483
Main 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
arxiv created 2020/04/08 · arxiv updated 2020/04/09
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.