5. Borromean Rings

5.1. Other Connections. This brings us back to finite constructions, based on polyhedra. And when we change the construction of the object in Figure 34 by replacing each ring by a pair of elements as shown in Figure 35, we are also back to our grids built with bars. The only difference with the bar grids in Section 1 is that the bars are bent. We can choose where we want to make the bending in the bar and this will give the object a different look. The object in Figure 35c comes close to the shape of a cube.
Figure 34: 6 Rings.
Figure 35a: 12 Bars.
Figure 35b: 12 Bars.
Figure 35c: 12 Bars.
5.2. Borromean Rings. A next step is to change the connection of the three bars that meet in a corner point of the cube. The midpoint of each hole in the bars is now situated exactly on the corner point of the cube. To make it fit we had to change the shape of the hole from circular to elliptic. It is still a ‘through and around weaving’ as defined in Section 1. The same connection is used in the dodecahedron structure of Figure 37. This special connection is in fact nothing more than the well known Borromean Rings (Figure 38).
Figure 36: Cubic structure.
Figure 37: Dodecahedron.
Figure 38: Borromean Rings.
5.3. Borromean Patterns. Starting with the Borromean Rings of Figure 39 we can develop the Borromean Pattern of Figure 40. Each ring in the pattern is used twice in a Borromean Ring connection. By changing the shape of the element as can be seen in the construction of Figure 41 these two connections are separated. In fact the element now connects two holes that can be used for a Borromean Ring connection. In the Borromean Joint of Figure 41 you can see very clearly that each of the elements is threaded through the hole of another element. With this element we can develop the 3-dimensional Borromean Pattern of Figure 42. The element can also be used to make the structure of Figure 43. An important difference between the two structures is that the structure of Figure 43 can be disassembled whereas the Borromean joint (Figure 44) cannot be taken apart.
Figure 39: Borromean Rings.
Figure 40: Borromean Pattern.
Figure 41: Borromean Joint.
Figure 42: Borromean Pattern.
Figure 43: Mortise and Tenon Joint.
Figure 44: Borromean Joint.