6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)
[Problem Session Notes]
Polyhedron refolding: Fractal unfolding, three boxes, flat boxes.
Kinetic sculpture: Theo Jansen's Strandbeests, Arthur Ganson.
This class starts with some updates on common unfoldings:
- 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.
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