5. Jitterbug

5.1. Jitterbug. Another transformation that can be used to create a serie of polyhedra is Buckminster Fuller’s Jitterbug transformation [4]. Starting with the octahedron the Jitterbug transformation brings us to the situation of Figure 14c in which the shape of the holes is exactly a square. At this point we can fill in those holes with square faces to get the cuboctahedron. An on this polyhedron we can again apply the Jitterbug transformation.
Figure 13a: Octahedron
Figure 13b: Opening
Figure 13c: Opening
Figure 13d: Cuboctahedron
Opening up the cuboctahedron until we reach the point that the spaces between the faces are exact squares, which can be filled in to create the rhomicuboctahedron.
Figure 14a: Cuboctahedron
Figure 14b: Opening
Figure 14c: Opening
Figure 14d: Rhombicuboctahedron
6. Splitting Polyhedra

6.1. Rhombicuboctahedron. Because the rhombicuboctahedran is two-colourable it can be split up into two groups of faces. This leads to an interesting construction.
Figure 15: Splitting up the Rhombicuboctahedron
We can build up each of the groups as a slide-together construction and so we get two spheres. When we want to do that we have to add radial ridges to hold the structures together. And because these constructions slide together towards the centre of the sphere, the second sphere can also be built around the first one. This gives us the complete closed sphere of Figure 16c.
Figure 16a: First part
Figure 16b: Second part
Figure 16c: Complete Polyhedron
It seems to be the only way to get all the pieces together to make this final construction. And this method can be applied on all the other 2-colorable polyhedra as can be seen in the next example.