8. Further steps

8.1. Alternate shapes. To open up the field for further research I experimented with some other shapes. The first group is a special set of star shaped polyhedra. The objects are constructed by applying a certain transformation to the octahedron, the cube and the dodecahedron. All three shapes can be assembled with a kind of pyramid shape. In each object the separate pieces will slide towards the center at the same time.

8.2. Escher's star - Rhombic star. Besides other shapes of the pieces also other types of movements can be studied to find new possibilities. The 12-pointed star that M.C. Escher uses in his print "Gravitation" [3] can be made from 12 flat pentagonal shapes. The question is whether it is possible to slide the pieces together to become the complete star. I decided to study the rhombic version of the 12-pointed star and found out that it was even possible to create an object with smaller holes then M.C. Escher used. The Rhombic star can be made as a slide together structure. But now we have to slide the pieces together not only by translation but we also have to rotate the pieces during the translation. It is a nice spiraling movement, which brings all the pieces smoothly together to a 12-pointed rhombic star. And in a way this brings us back to the beginning where as apart from the moving aspect there is a clear connection between this object and some of George Hart's sculptures [4].

Special thanks to Tom Longtin for helping me with the realization of some of the models.