# InfoCoBuild

## 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra

6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012, MIT OCW). Instructor: Professor Erik Demaine. 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. (from ocw.mit.edu)

 Lecture 17 - Alexandrov's Theorem

This lecture addresses the mathematical approaches for solving the decision problem for folding polyhedra. A proof of Alexandrov's Theorem and later a constructive version of Alexandrov is presented. Gluing trees and rolling belts are introduced.

 Class 17 - D-Forms

This class introduces the pita form and Alexandrov-Pogorelov Theorem. D-forms are discussed with a construction exercise, followed by a proof that D-form surfaces are smooth and are the convex hull of the seam. Rolling belts are addressed at the end.

Go to the Course Home or watch other lectures:

 Lecture 01 - Overview Lecture 02 - Simple Folds Lecture 03 - Single-Vertex Crease Patterns Lecture 04 - Efficient Origami Design Lecture 05 - Artistic Origami Design Lecture 06 - Architectural Origami Lecture 07 - Origami is Hard Lecture 08 - Fold & One Cut Lecture 09 - Pleat Folding Lecture 10 - Kempe's Universality Theorem Lecture 11 - Rigidity Theory Lecture 12 - Tensegrities & Carpenter's Rules Lecture 13 - Locked Linkages Lecture 14 - Hinged Dissections Lecture 15 - General & Edge Unfolding Lecture 16 - Vertex & Orthogonal Unfolding Lecture 17 - Alexandrov's Theorem Lecture 18 - Gluing Algorithms Lecture 19 - Refolding & Smooth Folding Lecture 20 - Protein Chains Lecture 21 - HP Model & Interlocked Chains