arXiv:2603.09813 · v4

Prismatoid Band-Unfolding Revisited

首次提交 2026-03-10 23:40

版本更新 2026-10-27 21:55

雷达观测 2026-10-29 00:34

摘要

It remains unknown if every prismatoid has a nonoverlapping edge-unfolding, a special case of the long-unsolved "Dürer's problem." Recently nested prismatoids have been settled [Rad24] by mixing (in some sense) the two natural unfoldings, petal-unfolding and band-unfolding. Band-unfolding fails due to a specific counterexample [O'R13b]. The main contribution of this paper is a characterization when a band-unfolding of a nested prismatoid does in fact result in a nonoverlapping unfolding. In particular, we show that the mentioned counterexample is in a sense the only possible counterexample. Although this result does not expand the class of shapes known to have an edge-unfolding, its proof expands our understanding in several ways, developing tools that may help resolve the non-nested case.

作者备注：Sadegh Merati found a counterexample to Lemma 8. Until I revise the argument, it is safest to withdraw