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