I feel like the next Voyager type vessel should include this shape made from gold or titanium or something. Also add an Einstein-tile. What more should we include?

Perhaps that knot that has a none additive “unknot” from a recent Stand-up Maths episode as well…

All Easter-eggs from our universe we found so far.

Misleading title. Other shapes have been well known for years, like a sphere. The novelty here is the first polyhedron that can't pass through itself.

Rather interesting solution to the problem. You can't test every possibility, so you pick one and get to rule out a bunch of other ones in the same region provided you can determine some other quality of that (non) solution.

I watched a pretty neat video[0] on the topic of ruperts / noperts a few weeks ago, which is a rather fun coincidence ahead of this advancement.

[0] https://www.youtube.com/watch?v=QH4MviUE0_s

In case someone is searching for the computational part of the proof, its on GitHub, implemented using SageMath: https://github.com/Jakob256/Rupert

I really like the level of detail in this article. It was enough that I felt like I could get an actual understanding of the work done, but not into such mathematical detail that it was difficult to follow.

Showing animation for every other shape but one that found, why

I'd only heard of Prince Rupert because of his eponymous "prince Rupert's drops", but apparently he had not just one but several dazzling careers https://en.wikipedia.org/wiki/Prince_Rupert_of_the_Rhine

Bah, but with those two flat sides I cannot use it for D&D! I’m really rooting for you, rhombicosidodecahedron!

Are there other mathematical discoveries that came from the result of a wager?

Given how hard it was to find one example, the next result is bound to be something like "almost all convex polyhedra cannot pass through themselves".

Layperson question: aren't the nopert candidates just increasingly close to being spheres, which cannot have Rupert tunnels?

Does it have to be straight through? I can imagine a scenario where the moving shape has to be rotated as it passes through. sort of analogous to some of those block puzzles or getting a sofa around a corner.

The article does say straight through and most analyses has been done with variation of the shadow technique, which has to be straight through. But the original bet. The thing that started this whole line of thought just said you had to get one through its copy, I think rotating is is an acceptable technique in this problem.

This was discussed on HN previously https://news.ycombinator.com/item?id=45057561

And I thought that the paper http://arxiv.org/abs/2508.18475 had also been discussed but can’t find it so could be wrong

Sorry for the silly question, but why spend time on this? Is it just for fun or is all mathematical exploration eventually useful? This feels closer to art than engineering.

I'd love to have an in-print magazine with articles of this subject matter and level of detail. Especially for older kids...accessible and interesting content without all the internet's distractions.

Googling says Quanta is online only. Anyone know of similar publications that print?

The triakis tetrahedron fit really is crazy close: https://youtu.be/jDTPBdxmxKw

What, I can't believe no one came with a term like "anisotransient" for such a property.

What about the sphere? Surely a hole bored through a sphere, no matter its size, could not pass a sphere of equal size?

> Noperthedron (after “Nopert,” a coinage by Murphy that combines “Rupert” and “nope”).

A good sense of humor to go with the math.

Presumably a simple sphere would trivially qualify as being unable to pass through itself.

> a researcher at A&R Tech, an Austrian transportation systems company

Austrian transport companies research this stuff?!?

I’m both impressed and confused

Prince Rupert was an incredibly interesting character. This problem was a minor footnote in an impressively rich life.

Fans of "Tom7" should be very recently familiar with this!

He released a video about the Ruperts problems and his attempt to find a Nopert on just Sept 16th!

https://www.youtube.com/watch?v=QH4MviUE0_s

With this and the Knotting conjecture being disproven, there are have some really interesting math developments just recently!

Tom regularly releases wonderful videos to go with SIGBOVIK papers about fun and interesting topics, or even just interesting narratives of personal projects. He has that weird kind of computer comedy that you also get from like Foone, the kind where making computers do weird things that don't make sense is fun, the kind where a waterproof RJ45 to HDMI adapter (passive) tickles that odd part of your brain.

The sphere and anything cylindrical...

What does this mean? Does it mean that an object can pass through the largest 2D projection of itself?

So disappointing to not have the 3D printer STL file for this shape. Wish they would have uploaded it to thingiverse or something.

He did it!!

it intuitively feels impossible because it sounds like the definition of "can pass through itself" is really "has at least one orientation where all of the sides of one instance are at most as long as all of the sides of the other instance" and then however you define an orientation an instance of a shape in orientation X should be able to pass through an instance of the same shape and size in the same orientation

>Prince Rupert of the Rhine, a 17th-century army officer, naval commander, colonial governor and gentleman scientist, won a bet about whether it’s possible to pass a cube through another.

Based.