Self-foldability of monohedral quadrilateral origami tessellations

TL;DR

This paper investigates the conditions under which certain monohedral quadrilateral origami tessellations can self-fold uniquely, revealing that symmetry plays a key role in their foldability properties.

Contribution

It introduces a mathematical model to determine self-foldability of monohedral quadrilateral tessellations, identifying which patterns are uniquely self-foldable based on symmetry.

Findings

Miura-ori and Chicken Wire are not self-foldable under the model

Rotationally symmetric tilings are uniquely self-foldable

Symmetry influences self-foldability of origami tessellations

Abstract

Using a mathematical model for self-foldability of rigid origami, we determine which monohedral quadrilateral tilings of the plane are uniquely self-foldable. In particular, the Miura-ori and Chicken Wire patterns are not self-foldable under our definition, but such tilings that are rotationally-symmetric about the midpoints of the tile are uniquely self-foldable.