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

TL;DR

This paper introduces two new infinitely refinable families of quad-mesh rigid origami generated from linear and equimodular couplings, expanding the design space beyond traditional patterns and conjecturing convergence to special ruled surfaces.

Contribution

It presents novel infinitely refinable origami families from linear and equimodular couplings, extending the known variations of quad-mesh rigid origami.

Findings

New families of infinitely refinable quad-mesh origami introduced.

Conjecture that refined meshes converge to special ruled surfaces.

Supports for convergence hypothesis provided through multiple evidence lines.

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.