Biplanar Foldings

TL;DR

This paper introduces a general framework for creating bifoldable polyhedra and complexes, extending origami patterns like Miura and Eggbox, with new examples of periodic and fractal structures.

Contribution

It presents a novel, broad framework for bifoldable structures, expanding beyond traditional origami patterns to include new periodic and fractal polyhedra.

Findings

Framework for bifoldable polyhedra and complexes

New examples of triply periodic bifoldable structures

Introduction of fractal bifoldable polyhedra

Abstract

We are introducing a general framework for the construction of polyhedra and simplicial comlexes that are {\em bifoldable}, i.e. foldable into two two different planes. This vastly generalizes Origami folds known as the Miura pattern, the Eggbox pattern. After describing the framework and its basic features, we give several new examples of infinite triply periodic and fractal bifoldable polyhedra.