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

Prof. Erik Demaine TA: Jayson Lynch

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[+] Polyhedron unfolding: Topologically convex vertex-ununfoldable polyhedron; unfolding orthogonal polyhedra with quadratic refinement.

This class covers two new results about unfolding, one negative and one positive:

There is a topologically convex polyhedron with no vertex unfolding. [Abel & Demaine 2011]
Orthogonal polyhedra can be unfolded with only quadratic (instead of exponential) refinement. [Damian, Demaine, Flatland 2012]

We'll also briefly discuss:

Why vertex unfoldings are so far “linear”
Why vertex unfoldings revisit vertices
Whether orthogonal unfoldings are practical
Whether other lattice polyhedra can be unfolded
Whether Cauchy's Rigidity Theorem is obvious

Download Video: 360p, 720p

Handwritten notes, page 1/3 • [previous page] • [next page] • [PDF]

Slides, page 1/24 • [previous page] • [next page] • [PDF]

The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The handwritten notes and slides should advance automatically. If you have any trouble with playback, email Erik.