A Universal Crease Pattern for Folding Orthogonal Shapes

TL;DR

This paper introduces a universal crease pattern based on tetrakis tiling that can fold into any polycube composed of unit cubes, simplifying origami design for complex shapes.

Contribution

It presents the first universal finite crease pattern for folding any polycube, advancing origami design by unifying multiple shapes into a single pattern.

Findings

Universal crease pattern exists for each number of unit cubes

Pattern can fold into any polycube made of unit cubes

Confirms the power of box pleating in origami design

Abstract

We present a universal crease pattern--known in geometry as the tetrakis tiling and in origami as box pleating--that can fold into any object made up of unit cubes joined face-to-face (polycubes). More precisely, there is one universal finite crease pattern for each number n of unit cubes that need to be folded. This result contrasts previous universality results for origami, which require a different crease pattern for each target object, and confirms intuition in the origami community that box pleating is a powerful design technique.