On Flat Polyhedra deriving from Alexandrov's Theorem
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 July 2010
 arXiv:
 arXiv:1007.2016
 Bibcode:
 2010arXiv1007.2016O
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics;
 51M20;
 F.2.2;
 G.2
 EPrint:
 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