Band Unfoldings and Prismatoids: A Counterexample
Computational Geometry
2007-10-04 v2
Abstract
This note shows that the hope expressed in [ADL+07]--that the new algorithm for edge-unfolding any polyhedral band without overlap might lead to an algorithm for unfolding any prismatoid without overlap--cannot be realized. A prismatoid is constructed whose sides constitute a nested polyhedral band, with the property that every placement of the prismatoid top face overlaps with the band unfolding.
Keywords
Cite
@article{arxiv.0710.0811,
title = {Band Unfoldings and Prismatoids: A Counterexample},
author = {Joseph O'Rourke},
journal= {arXiv preprint arXiv:0710.0811},
year = {2007}
}
Comments
5 pages, 3 figures. v2 replaced Fig.1(b) and Fig.3 to illustrate the angles delta=(1/2)epsilon (rather than delta=epsilon)