Catalog

Geometric Folding Algorithms: Linkages, Origami, Polyhedra

Electrical Engineering and Computer Science MIT CC BY-NC-SA 4.0 40 lectures

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.

Syllabus

  1. 1 Class 1: Overview
  2. 2 Class 2: Universality & Simple Folds
  3. 3 Class 3: Single-Vertex Crease Patterns
  4. 4 Class 4: Efficient Origami Design
  5. 5 Class 5: Tessellations & Modulars
  6. 6 Class 6: Architectural Origami
  7. 7 Class 7: Origami is Hard
  8. 8 Class 8: Fold & One Cut
  9. 9 Class 9: Pleat Folding
  10. 10 Class 10: Kempe's Universality Theorem
  11. 11 Class 11: Generic Rigidity
  12. 12 Class 12: Tensegrities
  13. 13 Class 13: Locked Linkages
  14. 14 Class 14: Hinged Dissections
  15. 15 Class 15: General & Edge Unfolding
  16. 16 Class 16: Vertex & Orthogonal Unfolding
  17. 17 Class 17: D-Forms
  18. 18 Class 19: Refolding & Kinetic Sculpture
  19. 19 Class 20: 3D Linkage Folding
  20. 20 Lecture 1: Overview, 6.849 Fall 2012
  21. 21 Lecture 2: Simple Folds
  22. 22 Lecture 3: Single-Vertex Crease Patterns
  23. 23 Lecture 4: Efficient Origami Design
  24. 24 Lecture 5: Artistic Origami Design
  25. 25 Lecture 6: Architectural Origami
  26. 26 Lecture 7: Origami is Hard
  27. 27 Lecture 8: Fold & One Cut
  28. 28 Lecture 9: Pleat Folding
  29. 29 Lecture 10: Kempe's Universality Theorem
  30. 30 Lecture 11: Rigidity Theory
  31. 31 Lecture 12: Tensegrities & Carpenter's Rules
  32. 32 Lecture 13: Locked Linkages
  33. 33 Lecture 14: Hinged Dissections
  34. 34 Lecture 15: General & Edge Unfolding
  35. 35 Lecture 16: Vertex & Orthogonal Unfolding
  36. 36 Lecture 17: Alexandrov's Theorem
  37. 37 Lecture 18: Gluing Algorithms
  38. 38 Lecture 19: Refolding & Smooth Folding
  39. 39 Lecture 20: Protein Chains
  40. 40 Lecture 21: HP Model & Interlocked Chains

Course materials