# Geometric Folding Algorithms: Linkages, Origami, Polyhedra

- Institution: Massachusetts Institute of Technology
- Department: Electrical Engineering and Computer Science
- Teacher: Prof. Erik Demaine
- Term: Fall 2012
- Level: Graduate
- Language: English
- Subjects: Mathematics, Computer science, Engineering, Art, architecture and design
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/)
- Licence: [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) (Non-commercial use only.)
- Syllabus: [at the source](https://ocw.mit.edu/courses/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/pages/syllabus/)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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.

Acknowledgments

Thanks to videographers Martin Demaine and Jayson Lynch.

## Lectures

1. [Lecture 1: Overview, 6.849 Fall 2012](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/1ce06482279f), 1 h 20 min (Video)
2. [Lecture 2: Simple Folds](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/fbaa02abf679), 1 h 24 min (Video)
3. [Lecture 3: Single-Vertex Crease Patterns](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/80b49f7becf9), 1 h 24 min (Video)
4. [Lecture 4: Efficient Origami Design](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/f8cf2bc96380), 1 h 27 min (Video)
5. [Lecture 5: Artistic Origami Design](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/619342735178), 1 h 27 min (Video)
6. [Lecture 6: Architectural Origami](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/c06814a92f86), 1 h 19 min (Video)
7. [Lecture 7: Origami is Hard](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/2892b4d51b43), 1 h 23 min (Video)
8. [Lecture 8: Fold & One Cut](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/369c3b834533), 1 h 21 min (Video)
9. [Lecture 9: Pleat Folding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/f5674819632b), 1 h 23 min (Video)
10. [Lecture 10: Kempe's Universality Theorem](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/b51e406f62d7), 1 h 19 min (Video)
11. [Lecture 11: Rigidity Theory](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/ed6fdf20aab8), 1 h 25 min (Video)
12. [Lecture 12: Tensegrities & Carpenter's Rules](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/90697996d27c), 1 h 25 min (Video)
13. [Lecture 13: Locked Linkages](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/cc0dd2d28cd7), 1 h 22 min (Video)
14. [Lecture 14: Hinged Dissections](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/f91fc59bb935), 1 h 22 min (Video)
15. [Lecture 15: General & Edge Unfolding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/21a0ffb905d2), 1 h 21 min (Video)
16. [Lecture 16: Vertex & Orthogonal Unfolding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/b52e645285be), 1 h 23 min (Video)
17. [Lecture 17: Alexandrov's Theorem](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/cc91f2015f19), 1 h 22 min (Video)
18. [Lecture 18: Gluing Algorithms](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/5ec71e085299), 1 h 22 min (Video)
19. [Lecture 19: Refolding & Smooth Folding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/8c3c82ecb613), 1 h 26 min (Video)
20. [Lecture 20: Protein Chains](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/e5cb24289bba), 1 h 20 min (Video)
21. [Lecture 21: HP Model & Interlocked Chains](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/9dfe3ca24a56), 1 h 10 min (Video)
22. [Class 1: Overview](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/496064808588), 51 min (Video)
23. [Class 2: Universality & Simple Folds](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/55dd910c0614), 54 min (Video)
24. [Class 3: Single-Vertex Crease Patterns](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/4611a1cb672f), 47 min (Video)
25. [Class 4: Efficient Origami Design](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/d47cc7107a4c), 50 min (Video)
26. [Class 5: Tessellations & Modulars](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/aeafed2b579c), 39 min (Video)
27. [Class 6: Architectural Origami](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/87b6b83a88ad), 46 min (Video)
28. [Class 7: Origami is Hard](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/4092c3ba7664), 50 min (Video)
29. [Class 8: Fold & One Cut](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/ddfc5bfe15e9), 50 min (Video)
30. [Class 9: Pleat Folding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/87a85692999e), 47 min (Video)
31. [Class 10: Kempe's Universality Theorem](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/00f3055c9f95), 45 min (Video)
32. [Class 11: Generic Rigidity](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/f9cecaf5c4a6), 51 min (Video)
33. [Class 12: Tensegrities](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/dedcdd68bf71), 19 min (Video)
34. [Class 13: Locked Linkages](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/4c4eb57a90d1), 52 min (Video)
35. [Class 14: Hinged Dissections](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/358a33142bf5), 53 min (Video)
36. [Class 15: General & Edge Unfolding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/5f9bdb527096), 51 min (Video)
37. [Class 16: Vertex & Orthogonal Unfolding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/9cac9124b25a), 42 min (Video)
38. [Class 17: D-Forms](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/7301670fd7e7), 44 min (Video)
39. [Class 19: Refolding & Kinetic Sculpture](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/2ef2eb5b1ea9), 32 min (Video)
40. [Class 20: 3D Linkage Folding](https://invisiblenetwork.ai/learn/mit/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012/33026a8f8f19), 39 min (Video)