Abstract
Twisted filaments are common structures in nature. We describe a geometric method of their creation, such that they possess a predefined polyhedral symmetry.
We start from a well-chosen polyhedron mapped to a circumscribed 2-sphere. The images of the vertices on the 2-sphere create circular fibers in a 3-sphere in the Hopf fibration.
Moreover, circles around the vertices form torus filaments around the fibers. After all, we visualize the filaments inside of the 3-sphere in a double-orthogonal and stereographic projection.