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    $\begingroup$ This is a series of questions, one for each convex polyhedron, rather than a single question. I don't think any one that is still open was asked in the 17th century. (The question about whether all convex polyehdra have this property is no longer open, and was asked in 2017.) $\endgroup$ Commented Oct 25, 2025 at 14:16
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    $\begingroup$ @Will Sawin: According to V. I. Arnold, a good problem is not a yes/no question, but a direction of research. Every mathematician, once s/he learns about Prince Rupert result, will immediately ask herself "which convex polytopes have this property?". $\endgroup$ Commented Oct 25, 2025 at 17:37
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    $\begingroup$ I would be happy with such logic if I ask the question, so I voted up. However, the given question explicitly ask that "There should be a clear record of the problem being formulated as a conjecture or question (as opposed to "so-and-so surely would have considered X after studying y".)" $\endgroup$ Commented Oct 26, 2025 at 7:44
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    $\begingroup$ @Bogdan Grechuk: So it remains to find Wallis' paper and check whether he asks the general question there:-) $\endgroup$ Commented Oct 26, 2025 at 13:08
  • $\begingroup$ I like this problem, although it's ironic that it wasn't posted here until arguably the biggest open problem in the area (does there exist a convex polytope without the Rupert property) was solved... $\endgroup$ Commented Oct 27, 2025 at 14:34