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.
- Pub Date:
- July 2010
- Computer Science - Computational Geometry;
- Computer Science - Discrete Mathematics;
- 8 pages, 3 figures, 10 references. This is a revision of the 2010 note, to clarify the meaning of 'n' in the complexity claim. Previously n was the number of vertices of the polygons, but n should be the complexity of the gluing instructions, which could be arbitrarily larger than the number of polygon vertices