  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.
