Steffen polyhedron

I have learnt about Steffen's polyhedron in my very first informatics lecture by Achim Clausing at the university. Since then I found this a very interesting object, as it is the most accessible of all flexible polyhedra. Cauchy proved (the modern version of the proof is considered to be contained in the BOOK (Chapter 12 in "Proofs from the Book")) that a convex polyhedron cannot be flexible. Steffen's polyhedron is very much non-convex, and thus it is hard to make pictures of it. I wanted to have a clear idea about its shape, and thus have built one out of paper, and more recently S&A helped me building a bigger one out of wood with metal hinges.

Here are three views of the big polyhedron:

View 1 of the big polyhedron model View 2 of the big polyhedron model View 3 of the big polyhedron model

Here are two videos where you can see the range of motion of both the paper model and the wooden one: Moving paper model, Wooden model.

Last modified: Sat Sep 07 15:52:48 CEST 2019