Band Unfoldings and Prismatoids: A Counterexample

Published 3 Oct 2007 in cs.CG | (0710.0811v2)

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.

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