Infinitely refinable generalization of quad-mesh rigid origami: from linear and equimodular couplings
Abstract
A quad-mesh rigid origami is a continuously deformable panel-hinge structure where planar, rigid, zero-thickness quadrilateral panels are connected by rotational hinges in the combinatorics of a grid. This article provides a comprehensive exposition of two new families of infinitely refinable quad-mesh rigid origami, generated from linear and equimodular couplings. These constructions expand the current landscape beyond well-known variations such as the Miura-ori, V-hedron (discrete Voss surface or eggbox pattern), anti-V-hedron (flat-foldable pattern), and T-hedron (trapezoidal pattern). We conjecture that as the mesh is refined to infinity, these quad-mesh rigid origami converges to special ruled surfaces in the limit, supported by multiple lines of evidence.
Cite
@article{arxiv.2412.04298,
title = {Infinitely refinable generalization of quad-mesh rigid origami: from linear and equimodular couplings},
author = {Zeyuan He and Kentaro Hayakawa and Makoto Ohsaki},
journal= {arXiv preprint arXiv:2412.04298},
year = {2025}
}
Comments
main text 21 pages (including references), supplementary material 74 pages, 20 figures, submitted manuscript