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arXiv · 2412.04298

Infinitely refinable generalization of quad-mesh rigid origami: from linear and equimodular couplings

Zeyuan He·Kentaro Hayakawa·Makoto Ohsaki
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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.

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Zeyuan He, Kentaro Hayakawa, Makoto Ohsaki. 2024-12-05. Infinitely refinable generalization of quad-mesh rigid origami: from linear and equimodular couplings. https://arxiv.org/abs/2412.04298

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