Symmetric 3-periodic polycatenanes: catenated rings, polyhedra and rods

We report symmetric (vertex- and arc-transitive) embeddings of catenated rings, polyhedra and rods. Linked triangles form infinite families of structures, and we limit this report to only structures with each ring linked to three or six others. For linked squares, hexagons, tetrahedra, octahedra, cubes and rods, only a small number of symmetric structures were found, and all are reported.