One-DOF Rigid and Flat-Foldable Origami Polyhedrons with Slits

Rigid origami has great potential in aerospace applications, especially deployable polyhedrons with one degree of freedom (DOF) and flat-foldability, whose types are few to date. In this paper, we create a novel foldable cube and a rhombic dodecahedron by introducing slits and diagonal creases to the surfaces, whose one-DOF rigid and flat-foldable properties are verified by kinematic analysis. Then, based on the isohedral quadrilateral transform, we project the creases and slits of the rhombic dodecahedron onto a tetrahedron to obtain a novel foldable tetrahedron that has two flat-foldable motion paths due to the existence of collinear creases. Following the second path, unnecessary creases are removed, and an origami tetrahedron with simplified creases is constructed. Both origami tetrahedrons possess a small folded area. Kinematic analysis reveals that these newly discovered origami polyhedrons are flat-foldable with one DOF, demonstrating favorable application prospects for space architectures and extraterrestrial habitats.