6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)

• The fractal unfolding of a cube and a regular tetrahedron is still a conjecture, but it is known to work for a tetrahedron that is within 1796 orders of magnitude of regular. [Shirakawa, Horiyama, Uehara 2011]
• We now have common unfoldings of three boxes. In fact, we have infinitely many examples. [Shirakawa & Uehara 2012]
• For flat boxes (doubly covered rectangles), we can even get common unfoldings of n boxes for any n. [Abel, Demaine, Demaine, Matsui, Rote, Uehara 2011]

Then, as a transition back to linkage folding (the next two lectures), we cover the beautiful leg mechanism of Theo Jansen's Strandbeests, and briefly review some of Arthur Ganson's kinetic sculptures.