On Flat Polyhedra deriving from Alexandrov's Theorem
Joseph O’Rourke · arXiv (Cornell University) · 2010
We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n^3) time for polygons whose gluings are specified by n labels.