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  "body": "\n## Statement\n\nEvery three-dimensional [[convex polytope|300K6CB1KH]] in $\\R^3$ has a [[net|FXJ66Z6PQY]].\nThat is, some spanning tree of its edge graph gives an edge unfolding without overlap.\n\n## Remarks\n\nThe conjecture is open.\nIt is named after Albrecht Dürer, whose book on geometry drew nets of many polyhedra, but it was first stated as a question by Shephard.\nCuts may also be allowed to run across faces and not only along edges.\nThen every convex polyhedron can be unfolded without overlap, for example by the source unfolding or the star unfolding.\nConvexity matters: there are non-convex polyhedra whose edge unfoldings all overlap.\nFor a given convex polyhedron, some spanning trees may give overlapping unfoldings, so the question is whether at least one good tree always exists.\n\n## Explanations\n\n### L1 human\n\nCan every convex solid with flat faces be cut along some of its edges and flattened into a single piece of paper with no part lying on top of another?\nFor the cube and all the familiar solids the answer is yes.\nNobody knows whether it is true for every convex solid, and no counterexample has been found.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "about": [
      "FXJ66Z6PQY"
    ],
    "history": {
      "first_stated": "1975",
      "posed_by": "Geoffrey Colin Shephard"
    },
    "kind": "conjecture",
    "msc": [
      "52B10",
      "52B05"
    ],
    "name": "Dürer's conjecture",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Net_(polyhedron)"
      }
    ],
    "tag": "PEDBPRSV9V",
    "uses": [
      "FXJ66Z6PQY",
      "300K6CB1KH"
    ]
  },
  "kind": "conjecture",
  "link": "https://tamnd.github.io/math2/node/PEDBPRSV9V/",
  "links": [
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      "field": "about",
      "target": "FXJ66Z6PQY"
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      "target": "FXJ66Z6PQY"
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      "field": "uses",
      "target": "300K6CB1KH"
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  "markdown": "https://tamnd.github.io/math2/node/PEDBPRSV9V.md",
  "msc": [
    "52B10",
    "52B05"
  ],
  "name": "Dürer's conjecture",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/PED/PEDBPRSV9V.md",
  "status": null,
  "tag": "PEDBPRSV9V",
  "uri": "m2://PEDBPRSV9V",
  "url": "https://tamnd.github.io/math2/wiki/durers-conjecture/",
  "writing": {
    "tag": "PEDBPRSV9V",
    "kind": "conjecture",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
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      {
        "what": "a source with a locator",
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