Lecture 16: Vertex & Orthogonal Unfolding
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Video Lecture 31 of 40
Copyright Information: Erik Demaine. 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 25 Jan, 2015). License: Creative Commons BY-NC-SA
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Date Added: January 25, 2015

### Lecture Description

This lecture continues with open problems involving general unfoldings of polyhedra and proof of vertex unfolding using construction of facet-paths. Approaches for unfolding orthogonal polyhedra, grid unfolding, and folding convex polyhedra are presented.

### Course Description

This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course.

This is an advanced class on computational geometry focusing on folding and unfolding of geometric structures including linkages, proteins, paper, and polyhedra. Examples of problems considered in this field include:

- What forms of origami can be designed automatically by algorithms?
- What shapes can result by folding a piece of paper flat and making one complete straight cut?
- What polyhedra can be cut along their surface and unfolded into a flat piece of paper without overlap?
- When can a linkage of rigid bars be untangled or folded into a desired configuration?

Many folding problems have applications in areas including manufacturing, robotics, graphics, and protein folding. This class covers many of the results that have been proved in the past few years, as well as the several exciting open problems that remain open.