First shape found that can't pass through itself
42 comments
·October 24, 2025king_geedorah
anyfoo
Not that coincidental. tom7 is mentioned in the article itself, and in his video's heartbreaking conclusion, he mentions the work presented in the article at the end. tom7 was working on proving the same thing!
teo_zero
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.
cluckindan
A sphere can be approximated by a polyhedron. Somewhat obviously, all such polyhedra would seem to have the Rupert property. This new Nopert seems to differ in one key detail: some of the vertices near the flat top/bottom are at a shallower angle to the vertical axis than the vertices below/above them.
Can you pass the T-shaped tetromino through itself?
mkl
The T-shaped tetromino is not convex, so not part of the conjecture. There are many nonconvex shapes that don't have the Rupert property.
jibal
convex polyhedron
(but your point about the title is valid)
cyode
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?
tempestn
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.
TheOtherHobbes
Prince Rupert was an incredibly interesting character. This problem was a minor footnote in an impressively rich life.
jmkd
Layperson question: aren't the nopert candidates just increasingly close to being spheres, which cannot have Rupert tunnels?
tmiku
Yes, they get visually more sphere-like as more faces are added. But spheres are obviously/trivially non-Rupert, while the question of whether a convex polyhedron can be non-Rupert is more interesting.
gitaarik
Would be interesting to see how much sides you can keep adding before the shape can't pass through itself. Or maybe you can indefinely keep passing them through, occasionally encountering noperts. Or maybe the noperts gradually increase, eventually making the no-nopperts harder to find. Who knows, let's find out.
maplant
But importantly, they’re NOT!
biot
Presumably a simple sphere would trivially qualify as being unable to pass through itself.
smokel
The puzzle applies only to convex polyhedra.
LostMyLogin
A sphere is not a convex polyhedron
dnw
> Noperthedron (after “Nopert,” a coinage by Murphy that combines “Rupert” and “nope”).
A good sense of humor to go with the math.
pinkmuffinere
Tom7 is one of my favorite people, he is hilarious, has an amazing technical depth, and so much whimsy to go along with it. I'll proselytize for him all day!
relevant video: https://www.youtube.com/watch?v=QH4MviUE0_s
less relevant, but I think my favorite: https://www.youtube.com/watch?v=ar9WRwCiSr0
867-5309
this logical falsehood annoyed me since nopert is no+Rupert, whereas nope+Rupert would in fact be nopepert
strbean
That's not how portmanteaus work.
stephenlf
Tom7 also has a couple of videos about portmanteaus
burkaman
The coiner gets to pick the combination that sounds the best, there is no correct choice. We could have gotten breakfunch and mototel, but some person or collection of people decided that brunch and motel work better.
jibal
Perhaps you should review what "logical falsehood" means, because that's not one.
pharrington
Portmanton't.
stephenlf
He did it!!
mrguyorama
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.
chaps
His videos are some of the best out there. Super funny, depth that's rarely seen elsewhere, and a refreshingly scrappy academic approach. His video on kerning being an incomputable problem is filled with rigor and worth a watch.
Highly recommend all of his videos!
null
ratelimitsteve
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
strbean
The criteria is "pass through itself without cutting in half". Presumably that extends to "without deleting the object entirely", which is what would happen to pass through in the same orientation.
jibal
Notably, a sphere is non-Rupert (but a soccer ball is not ... it can pass through a tiny fringe).
jibal
My intuition is very different (and happens to fit reality). Note that convex polyhedra can have asymmetries.
hyperhello
Yes, and when you think of it that way, it sounds like a partial ordering with a base case. If angle A can pass through angle B, and angle B can pass through angle C…
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