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Think of cutting open a cubical box with the smallest possible cuts to lay it flat. A cube has 12 edges and it seems in all the possible meshes, you have to cut along 7 edges. So, the most possible number of distinct ways to lay a cube flat should be ${12 \choose 7} = 792$. But some of these are ruled out. For instance, you can't cut one face completely off (by choosing all 4 of its edges for cuts). So, what are the total ways to make the cuts and lay the cube flat? Some of them are shown below (the meshes with ticks are possible and the one with the cross isn't).

EDIT: Per @OscarLanzi's comment, the number of distinct meshes is $11$. But there are multiple cuts that lead to each of those meshes. I'm looking for the number of ways to make the cuts. But also interested in how one would count the distinct meshes.

enter image description here

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    $\begingroup$ 5280math.com/nw-early-27-cube-nets $\endgroup$ Commented May 8, 2022 at 22:34
  • $\begingroup$ Thanks! How do I know I've found all 11? $\endgroup$ Commented May 8, 2022 at 23:02
  • $\begingroup$ This is a long solved problem, people who post this nowadays take it for granted. $\endgroup$ Commented May 9, 2022 at 0:02
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    $\begingroup$ @RohitPandey This video might interest you youtube.com/watch?v=Yq3P-LhlcQo $\endgroup$ Commented May 9, 2022 at 3:59

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Pasting the meshes from @OscarLazi's link as an answer.

enter image description here

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