Band Unfoldings and Prismatoids: A Counterexample

Details Band Unfoldings and Prismatoids: A Counterexample Band Unfoldings and Prismatoids: A Counterexample

2007-10-03

arxiv.org/abs/0710.0811v2

Computer Science

Computational Geometry

5 pages, 3 figures. v2 replaced Fig.1(b) and Fig.3 to illustrate the angles delta=(1/2)epsilon (rather than delta=epsilon)

Scientific paper

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.

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