Non-Euclidean Origami

TL;DR

This paper introduces non-Euclidean origami vertices that overcome traditional folding limitations, enabling more stable and versatile origami structures with potential applications like inverters and tristable vertices.

Contribution

It demonstrates how non-Euclidean 4-vertices improve folding stability and multistability, advancing origami design beyond Euclidean constraints.

Findings

Non-Euclidean 4-vertices lift degeneracy in folding motions.

Incorporation of hinge elasticity enables higher-order multistability.

Designed an origami inverter resistant to misfolding and realized a tristable vertex.

Abstract

Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how non-Euclidean 4-vertices overcome these limitations by lifting this degeneracy, and that when the elasticity of the hinges is taken into account, non-Euclidean 4-vertices permit higher-order multistability. We harness these advantages to design an origami inverter that does not suffer from misfolding and to physically realize a tristable vertex.