6.2. Rhombicosidodecahedron. When we split up this polyhedron in two groups of faces we get one sphere with only the square faces and another with the triangular and pentagonal faces. In Figure 17 you can see how the real model is put together. We start building up the first part of the sphere by connecting the triangle and the pentagonal faces with the radial ridges (Figure 17a). After the first part is finished (Figure 17b) we can start building up the second part (Figure 17c, 17d). We can build up the second around the first part and after we have put in the final pieces we can just squeeze the second part together to complete the construction.
Figure 17a: Starting to build the sphere
Figure 17b: First part
Figure 17c: Adding the second part
Figure 17d: Second part
Figure 17e: Almost finished
Figure 17f: Complete Polyhedron
We The model is build up during the Gathering for Gardner Conference (G4G10) in Atlanta in 2012. Some of the pictures were taken by Doris Schattschneider (17a, 17b and 17e).
7. Johnson Polyhedra

7.1. equal Groups. Besides the Platonian and the Archimedean polyhedra there are some more convex polyhedra that you can build using convex regular faces only. This group of polyhedra is known as the Johnson Polyhedra. Among the Johnson Polyhedra we can also find some members which are two-colourable. Some of them are shown in Figure 18.

Figure 18: Two-colourable Johnson solids
7.2. Pseudo RCO. The second example in the row shows the Pseudo Rhombicuboctahedron and this polyhedron deserves some extra attention. When we split it up in two parts, both parts are now identical.
Figure 19: TPseudo Rhombicuboctahedron split up in two identical parts

References

[1] M.C. Escher, Regelmatige Vlakverdeling, Stichting de Roos, 1958.
[2] Greg N. Frederickson, Hinged Dissections: Swinging and Twisting, Cambridge University Press, 2002.
[3] Wentzel Jamnitzer, Perspectiva corporum regularium, Ediciones Siruela, 1993, 2006.
[4] R. Buckminster Fuller, Synergetics, Macmillan Publishing, 1975.