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

Lecture 06 - Architectural Origami

This lecture presents Origamizer, freeform origami, and rigid origami applied to architectural and three-dimensional design contexts. Geometric constraints, demonstration videos, and physical models are shown for each portion of the lecture.

Class 06 - Architectural Origami

This lecture begins with a folding exercise and demonstration involving Origamizer. A high-level overview of the mathematical constraints for Freeform and Rigid software are presented, followed by examples of origami robots and current open problems.

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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