Biplanar Foldings

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.