Lecture 11: Vertex unfolding, unfolding orthogonal polyhedra; Cauchy's rigidity theorem, uniqueness of folding
Page 2: Construction of facet path in any simplicial manifold, existence of facet cycles
You can view the vertex-unfolding paper. Another paper by Bartholdi and Goldsman established similar results but in a different setting.
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.