Steffen's flexible polyhedron

thingiverse

About Steffen's Flexible Polyhedron ***** Steffen's polyhedron is a polyhedral surface with the remarkable property that it remains flexible, even with rigid faces. This means that it can still be continuously deformed by allowing only rotations of its faces around their shared edges. Unlike a cube or a pyramid which are perfectly rigid, Steffen's polyhedron showcases this unique characteristic. The first non-intersecting flexible polyhedron was discovered by Connelly in 1977, and the polyhedron designed here was subsequently constructed by Steffen in 1978. It turns out that Steffen's polyhedron is the simplest non-intersecting flexible polyhedron, featuring only 9 vertices and 14 faces. But of course, it is not convex at all! Some additional information includes: - Wolfram's demo - Paper cutout for Steffen's polyhedron - A survey about flexible polyhedrons (in French) - Scan of a handwritten letter where Steffen describes the polyhedron ***** About this design ***** It is easy and instructive to make a paper fold of Steffen's Polyhedron. However, I have always felt that the paper version is not rigid enough to really assert that the shape is changing via rotations around the edges and not also by bending the paper. Therefore, I decided to create a solid 3D print version of the polyhedron with hinges to allow rotations around the edges. There are two STL files provided: the first one for the polyhedron with solid faces and the second for the same polyhedron but with hollow faces instead. Both versions are based on the same design, so they can be mixed to create a polyhedron with both solid and hollow faces. ***** Material Needed ***** The assembly of the polyhedron requires some care (and some time). In addition to the printed parts, you will also need: - Many paper clips (or some straight wire with 0.8mm diameter) - A small drill bit (0.8/0.9 mm) - Pliers to secure the wire into the hinges