Phenomenal Three-Dimensional Objects

Abstract

Original thesis project: By studying the literature, collect and write a survey paper on special three-dimensional polyhedra and bodies. Read and understand the results, to which these polyhedra and bodies are related.

Although most of the famous examples are constructed in a very clever way, it was relatively easy to understand them. The challenge lied in the second half of the project, namely at studying the theory behind the models. I started to learn things related to Schonhardt's polyhedron, Csaszar's polyhedron, and a Meissner body. During Fall 2010 I was a frequent visitor of Dr. Bezdek's 2nd studio class at the Industrial Design Department where some of these models coincidently were fabricated. A change in the thesis project came while reading a paper of R. Guy about a polyhedron which was stable only if placed on one of its faces. It turned out that for sake of brevity many details were omitted in the paper, and that gave room for a substantial amount of independent work. As a result, the focus of the thesis project changed.

Modified thesis project: By studying the literature, write a survey paper on results concerning stable polyhedra.

The following is the outcome of the thesis: 1. A collection of elementary facts/theorems/proofs concerning stable tetrahedra. 2. A description of a double tipping tetrahedron constructed by A. Heppes. 3. A description of a 19 faceted polyhedron of R. Guy, which has only one stable face. 4. Description of the Gomboc, a recently discovered mono-monostatic 3D body.