3. Circular Bars

3.1. Circular Bars - vertical. In Figure 8 a new type of bar is introduced: a circular bar with holes. There are two main ways to make holes in circular bar: it can be done in the plane of the circle of the bar or perpendicular to the plane of the circle of the bar. The last case we will call ‘bars with vertical holes’. And now using Escher’s idea of distributing the holes on the bars we can make some nice ‘weaving’ patterns with circular bars. The examples show eight, six and five holes respectively (Figures 9 - 13).
Figure 8: Circular bar.
Figure 9a: Ring, 8 holes.
Figure 9b: Ring, 6 holes.
Figure 9c: Ring, 5 holes.
Figure 10a: Connecting rings ‘8’.
Figure 10b: Connecting rings ‘6’.
Figure 10c: Rings, '5'.
Figure 11: Weaving pattern ‘8’.
Figure 12: Weaving pattern ‘6’.
Figure 13: Weaving pattern ‘5’.
3.2. Circular Bars - horizontal. Connecting rings with horizontal holes will result in 3-dimensional objects. To make a design for a spherical ring structure you can start with a regular or semi regular polyhedron. There are, except for the anti prisms, five polyhedra that can be used to make a ring patterns on the sphere (Figure 14). The smallest of them, based on the octahedron, is a ring pattern with three rings, with four crossings each. This leads to the bar grid construction of Figure 15. Each ring has two horizontal holes (Figure 16).
Figure 14: Ring patterns on the spheres.
Figure 15: Three rings.
Figure 16: Two holes.
This is just a basic set up of a ‘through and around weaving’ with circular bars. Varying the design of the elements can give a very different look (Figure 17 and 18). But mathematically speaking it is the same object.
Figure 17a: Twisted band.
Figure 17a: Band with holes.
Figure 18: Final object.
The twist in the band is needed to get a nice ‘through and around weaving’. When you have an odd number of twists, which is the case when you start with the right most ring pattern of Figure 14, the icosidodecahedron, the rings becomes Moebius bands. We need six of these rings with five holes in each ring to construct the bar grid structure of the icosidodecahedron (Figure 20 and 21).
Figure 19: 6 Twisted bands.
Figure 20: Ring with holes.
Figure 21: Icosidodecahedron.