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  "path": "/abs/2603.09813v1",
  "publishedAt": "2026-03-11T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Joseph O'Rourke"
  ],
  "textContent": "**Authors:** Joseph O'Rourke\n\nIt 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.",
  "title": "Prismatoid Band-Unfolding Revisited"
}