On Flat Polyhedra deriving from Alexandrov's Theorem
Computational Geometry
2015-09-10 v2 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1007.2016,
title = {On Flat Polyhedra deriving from Alexandrov's Theorem},
author = {Joseph O'Rourke},
journal= {arXiv preprint arXiv:1007.2016},
year = {2015}
}
Comments
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