An Origami-Inspired Spherical Transformable Metamaterial Based on Symmetry Groups

Most currently existing mechanical metamaterial designs are based on Bravais lattices. These consist of parallelogram or parallelepiped unit cells, which are respectively translated along two or three independent vectors to fill the complete space. This approach is inherently unable to match curved surfaces like spheres, since these cannot be constructed only from parallel and perpendicular lines. In this paper, we introduce a generalized unit cell, based on the symmetry groups of the sphere. We use this approach to develop a spherical transformable origami-inspired metamaterial. We describe the motions of this new metamaterial, as well as experimental observations on a physical, 3D printed model.