Lecture 12: Flexible polyhedra, Bellows Theorem; folding polygons into polyhedra, gluings, convex polyhedral metrics, Aleksandrov's Theorem, Sabitov's algorithm, ungluable polygons
Page 1: Flexible polyhedra: not convex polyhedra if only finitely many creases, not generic triangulated polyhedra, paper bag, Bricard "octahedron", Connelly's flexible polyhedron, Steffen's flexible polyhedron. Bellows Theorem. Volume polynomials.
You can view illustrations of Bricard's flexible "octahedron", Connelly's flexible polyhedron, and Steffen's flexible polyhedron. You can view the paper proving the Bellows Conjecture.
You can view the Fedorchuk and Pak paper on volume polynomials and algorithms for Aleksandrov's Theorem, which also summarizes Sabitov's work.
These are rough, personal lecture notes handwritten by Erik Demaine used during lecture. Their primary purpose is for reading/review by students of the class.