CONTENTS Introduction 1 Part I. Linkages 1. Problem classification and examples 9 2. Upper and lower bounds 17 3. Planar linkage mechanisms 29 4. Rigid frameworks 43 5. Reconfiguration of chains 59 6. Locked chains 86 7. Interlocked chains 123 8. Joint-constrained motion 131 9. Protein folding 148 Part II. Paper 10. Introduction 167 11. Foundations 172 12. Simple crease patterns 193 13. General crease patterns 214 14. Map folding 224 15. Silhouettes and gift wrapping 232 16. The tree method 240 17. One complete straight cut 254 18. Flattening polyhedral 279 19. Geometric constructability 285 20. Rigid origami and curved creases 292 Part III. Polyhedra 21. Introduction and overview 299 22. Edge unfolding of polyhedral 306 23. Reconstruction of polyhedral 339 24. Shortest paths and geodesics 358 25. Folding polygons to polyhedral 381 26. Higher dimensions 437 Bibliography 443 Index 461