Talk:Prince Rupert's cube

GA Review

This review is transcluded from Talk:Prince Rupert's cube/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Ovinus (talk · contribs) 20:12, 30 June 2022 (UTC)

I can already think of a cute DYK hook: "Did you know that a cube can fit through itself?"

• "Pieter Nieuwland found the largest possible cube that can pass through a hole in a unit cube" Also say who and when this fact was proved; seems important Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • Finally found some time to work on this a little today. I found and added the original publication of Nieuwland's result but it's in Dutch so it's hard for me to tell exactly what is claimed. I did not find any source that mentioned Nieuwland at all but gave credit for the proof to anyone else; they all at least strongly suggest that Nieuwland knew his solution was optimal. —David Eppstein (talk) 06:11, 5 July 2022 (UTC)
• "Many other polyhedra have been shown to have the Rupert property" Say "including all five Platonic solids" or something, just so that the reader knows it's not about some boring or obscure polyhedra. Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • Sure, done. Also mentioned the unsolved problem of whether it is true for all polyhedra. —David Eppstein (talk) 06:11, 5 July 2022 (UTC)
    • Presumably you mean convex polyhedra in the lead? Or is that equivalent to the general case by taking convex hulls? That doesn't seem right to me, but I'm afraid I can't visualize it. Ovinus (talk) 17:07, 5 July 2022 (UTC)
      • I meant convex. I remembered to say convex once in that sentence, but forgot the second time. I have no idea what should be true in the non-convex case (assuming we could even agree on one of the many definitions for non-convex polyhedra) but taking convex hulls doesn't look likely to work. —David Eppstein (talk) 18:25, 5 July 2022 (UTC)
• When was Nieuwland's solution proven optimal? Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • See above. Presumably by Nieuwland, some time before he died, but I haven't found a clear explicit statement of that. I have no idea whether, if Nieuwland indeed had a proof, it would meet modern standards of rigor. —David Eppstein (talk) 06:11, 5 July 2022 (UTC)
• "Cubes and all rectangular solids have Rupert passages in every direction that is not parallel to any of their faces" But in which direction is the "Rupert ratio" maximized? Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • The one for Nieuwland's solution. That's what it means for it to be optimal. —David Eppstein (talk) 06:11, 5 July 2022 (UTC)
• "optimal rectangle must always pass through the center of the cube" Pass through, sure... but centered on? Being explicit here would help. Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • Ok, now "centered at the center". —David Eppstein (talk) 06:11, 5 July 2022 (UTC)
• "or must be formed by an isosceles right triangle on one corner of the cube and by the two opposite points" I don't really get what this means. Formed? As in the triangle and the rectangle lie in the same plane and share vertices? Can't visualize this Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • Rewritten. It doesn't mention the isosceles triangle any more, but it was intended to mean the 45-45-90 isosceles triangle that you get from cutting off a corner of a cube, at some distance from the corner. The base of this triangle is one edge of the rectangle, and its reflection across the center of the cube is the other edge. —David Eppstein (talk) 11:34, 5 July 2022 (UTC)
• "If the aspect ratio is not constrained, the rectangle with the largest area..." What is the aspect ratio of this optimal rectangle? Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • Added. —David Eppstein (talk) 11:34, 5 July 2022 (UTC)
• Specifically cite the Pythagorean theorem in the calculation of $3{\sqrt {2}}/4$, for the broadest accessibility Ovinus (talk) 20:12, 30 June 2022 (UTC)
  • Ok, done. There are actually two different calculations of this value, for two perpendicular sides of the square. —David Eppstein (talk) 11:34, 5 July 2022 (UTC)

A fun and accessible article. For some reason the article got tens of thousands of views on June12; do you know why? Ovinus (talk) 20:12, 30 June 2022 (UTC)

Thanks for starting this review! I'm about to go on some international travel so I may be a bit less responsive than usual over the next week or two. No idea re the page views. As for DYK, it's already been listed, so a second nomination would be disallowed. —David Eppstein (talk) 20:26, 30 June 2022 (UTC)

Sad... FAC? :P Anyway, bon voyage! Ovinus (talk) 20:28, 30 June 2022 (UTC)

• For the whole (m,n) hypercube generalization thing, is $\lim _{n\to \infty }f(n,n)=1$, or bounded away from one? Ovinus (talk) 17:07, 5 July 2022 (UTC)
  • I don't know. The Huber et al paper is not very explicit; their construction appears to converge to 1 but they don't prove that it's optimal. —David Eppstein (talk) 18:31, 5 July 2022 (UTC)
• One last thing, regarding cite [23]: is it okay to cite ArXiV preprints? I'd suggest adding an inline statement like "In a preprint, Smith & Doe (2020) found ... ", unless it's going to be published soon. But I'm not sure on the guidelines for this stuff. Ovinus (talk) 02:20, 6 July 2022 (UTC)
  • It's not a reliably published source, and (as its authors appear to be students) can't be squeezed in under the "established expert" clause of WP:SPS. I removed it. Pity, though, as I found the statistical evidence for some polyhedra not having the Rupert property to be interesting. —David Eppstein (talk) 04:53, 6 July 2022 (UTC)
    • Sad indeed... wondering whether it's appropriate to occasionally IAR and cite it (with inline attribution) for interesting but not highly questionable results. I think you accidentally removed some perfectly fine sources in that edit, the ones for the truncated tetrahedron. Once that's been addressed, I think I'll pass; am happy with the article. Ovinus (talk) 13:41, 6 July 2022 (UTC)
      • Oh, didn't see you did this on my watchlist. Passing! Ovinus (talk) 19:05, 9 July 2022 (UTC)

Blender animation

A blender animation of a unit cube (not Prince Rupert's which is bigger) passing through a hole in another unit cube. It would be cool to have an illustration like this of Prince Rupert's cube for the article. 2601:644:8581:75B0:5E3A:1231:9276:1405 (talk) 21:09, 22 August 2025 (UTC)

Better image for Noperthedron

While I appreciate having an illustration of Noperthedron, how about changing the sandy background to an SVG white background?. Dedhert.Jr (talk) 04:18, 27 October 2025 (UTC)

Unsolved template?

I don't have a strong opinion, but it's probably worthwhile to discuss whether to keep {{Unsolved}} in the article. Some arguments might be:

• Pro: The Noperthedron article hasn't been peer-reviewed. The template is useful to draw attention to this part of the process for a proof to gain acceptance, and even to highlight that the claim of a recent solution is noteworthy, by contrast with the status quo.
• Con: The popular press (Quanta, SciAm) have already run articles describing the problem as solved. They reached out to experts for quotes, and nobody cast any doubt on the result. It's safe for Wikipedia to defer to these sources; in fact, it's strange if we don't.

Melchoir (talk) 05:17, 29 October 2025 (UTC)

@Melchoir. And more strangely, our article List of unsolved problems in mathematics keep the Prince Rupert's cube's problem as unsolved. I retrieved the template for now. Dedhert.Jr (talk) 05:32, 9 January 2026 (UTC)

Sounds good to me! Melchoir (talk) 05:01, 10 January 2026 (UTC)

I removed the unsolved template from the section "Other polytopes," since that seemed to be the consensus here, and I also agree. CTourneur (talk) 04:19, 20 January 2026 (UTC)

Eh, I wouldn't say it's a mature consensus. It might be the preference of more than 50% of recent editors, but that's a weaker thing. Actually I'm starting to wonder if {{Unsolved}} itself should have a |tentative_solution= parameter to act as a compromise. Melchoir (talk) 04:37, 24 January 2026 (UTC)

Nieuwland constant

@David Eppstein. Our article does not explicitly state the definition of the Nieuwland constant, or synonymously the Nieuwland number. By writing it and some hits by Google Scholar , the article perhaps can be the core of calculating the hole in many polyhedra in practice. Dedhert.Jr (talk) 01:22, 4 February 2026 (UTC)