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.