Double-twist structures in vector fields with cubic symmetries: from the viewpoint of rod packings

Abstract

Invariant tori are nested tubelike surfaces wound around by integral curves of three-dimensional solenoidal vector fields and form double-twist structures. Arrangements of invariant tori that resemble cubic rod packings are found. What twists generate each of the rod-packing-like arrangements of invariant tori is made clear. The realization of the arrangements in electromagnetic fields is discussed.