Band Unfoldings and Prismatoids: A Counterexample
Abstract
Description
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.
5 pages, 3 figures. v2 replaced Fig.1(b) and Fig.3 to illustrate the angles delta=(1/2)epsilon (rather than delta=epsilon)
5 pages, 3 figures. v2 replaced Fig.1(b) and Fig.3 to illustrate the angles delta=(1/2)epsilon (rather than delta=epsilon)