There are two ways to connect rings with five holes in such a way that we get the structure of an Archimedean polyhedron as the final object (Figure 22). When we start connecting the rings as shown in Figure 22b we will need twelve rings and end up with a circular bar construction based on the rhombicosidodecahedron (Figure 23). In the example shown in Figure 24 you may not directly recognise the basic polyhedron. But it consists of four pairs of parallel rings, and the structure is based on the cuboctahedron (Figure 25a). When you use only single rings you will get the object of Figure 26.
Figure 22a: Connection 1.
Figure 22b: Connection 2.
Figure 23: Final object.
Figure 24: 8 Rings.
Figure 25a: Cuboctahedron and the twisted band.
Figure 25b: Band with holes.
Figure 26: Final object.
4. Infinite Ring Structures

4.1. Rings with three Holes. Four rings with three holes each can be used to construct the cuboctahedron structure of Figure 27. But we can also place the four rings on four of the hexagonal faces of the truncated octahedron as in Figure 28.
Figure 27: Cuboctahedron.
Figure 28a: Cuboctahedron.
Figure 28b: Cuboctahedron.
TAnd now, because of the space filling property of the truncated octahedron, we can build a infinite space structure with the rings by connecting groups of rings as is shown in Figure 29. A few pictures of the final structure are presented in Figures 30a and 30b.
Figure 29: Connecting groups.
Figure 30a: Infinite structure.
Figure 30b: Infinite structure.
4.2. Rings with two Holes. When we look at the steps we have taken to construct this structure, it is easy to understand that a similar structure can be made by starting to place rings with two holes on the square faces of the truncated octahedron. And this leads to the infinite structure of Figure 31.
Figure 31: Rings with two holes.
Figure 32: Infinite structure.
Figure 33: Rings with four holes.
Rings with two holes can be used in more than one way to construct an infinite structure. In Figure 32 a second possibility is shown. And from here on we can create the structure of Figure 33 by replacing each ring by a pair of parallel rings with four holes each. It is in the same step that you need if you want to develop the ring structure based on the rhombicuboctahedron (Figure 34). You start with the three ring structure of Figure 15, and replace each ring (with two holes) by a parallel set of rings with four holes each.