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First Shape Found That Can't Pass Through Itself (quantamagazine.org)

(Monday October 27, 2025 @06:50PM (msmash) from the you-shall-not-pass dept.)


Mathematicians have identified the first shape [1]that cannot pass through itself . Jakob Steininger and Sergey Yurkevich described the Noperthedron in a paper posted online in August. The shape has 90 vertices and 152 faces. The discovery resolves a question that began in the late 1600s when Prince Rupert of the Rhine won a bet by proving one cube could slide through a tunnel bored through another. Mathematician John Wallis confirmed this mathematically in 1693.

The property became known as the Rupert property. In 1968, Christoph Scriba proved the tetrahedron and octahedron also possess this quality. Over the past decade, researchers found Rupert tunnels through many symmetric polyhedra, including the dodecahedron and icosahedron. Mathematicians had conjectured every convex polyhedron would have the Rupert property. Steininger and Yurkevich divided the space of possible orientations into approximately 18 million blocks and tested each. None produced a passage. The Noperthedron consists of 150 triangles and two regular 15-sided polygons.



[1] https://www.quantamagazine.org/first-shape-found-that-cant-pass-through-itself-20251024/



Finally! (Score:5, Funny)

by GoTeam ( 5042081 )

We finally know how to keep Noperthedron shaped animals from using the doggie door!

More explanation (Score:5, Informative)

by Okian Warrior ( 537106 )

Imagine a black unit cube cake with white frosting. Take a knife and cut out pieces of the cube to make a black hole outline within the white frosting. When you do this at an angle to the sides, it turns out that [1]a cube 6% larger [wikipedia.org] than the original cube can pass through the outlined hole.

All the platonic solids have this property, along with a lot of other polyhedral solids.

[1] https://en.wikipedia.org/wiki/Prince_Rupert's_cube

Re: More explanation (Score:5, Funny)

by LindleyF ( 9395567 )

The cake is a lie!

Re:More explanation (Score:4, Interesting)

by nuckfuts ( 690967 )

> Imagine a black unit cube cake with white frosting. Take a knife and cut out pieces of the cube to make a black hole outline within the white frosting. When you do this at an angle to the sides, it turns out that [1]a cube 6% larger [wikipedia.org] than the original cube can pass through the outlined hole.

> All the platonic solids have this property, along with a lot of other polyhedral solids.

You can watch a physical demonstration of this [2]here [youtube.com].

It's quite a "hole", however. There's not a lot left of the original cube.

[1] https://en.wikipedia.org/wiki/Prince_Rupert's_cube

[2] https://www.youtube.com/watch?v=nWPdpqUEfE0

Re: (Score:3)

by TwistedGreen ( 80055 )

What if it's a cellular peptide cake with mint frosting?

Did they use AI? (Score:2)

by blue trane ( 110704 )

How can you know?

Re: (Score:1)

by wed128 ( 722152 )

I'm as anti-AI as the next guy, but in this case does it really matter?

Pedantic Correction (Score:4, Informative)

by necro81 ( 917438 )

The title says "First Shape Found That Can't Pass Through Itself". If we just went by the title, once could easily say "a sphere cannot pass through itself!" The summary clarifies by saying "convex polyhedron."

Re: (Score:2)

by votsalo ( 5723036 )

Isn't a sphere approximated by a series of convex polyhedrons with more and more vertices? For example, geodesic polyhedrons, where each one is formed by adding a vertex centered on each face, but on the surface of the sphere? Are these all Rupert objects, but the sphere that they converge to isn't?

Like a plane? Or a line? (Score:2)

by usedtobestine ( 7476084 )

Do I get two awards?

so when will we see a Rupert's cube? (Score:2)

by Provocateur ( 133110 )

Because calling the toy Rupert's Noperthedron, would be accurate but might fail to gain market traction.

But can you pass a billionaire through the eye of (Score:2)

by jlowery ( 47102 )

Let's try!

Prince Rupert's Drop (Score:2)

by thegreatemu ( 1457577 )

Almost completely off-topic, but one of Rupert's most famous contributions is Prince Rupert's drop. Cool molten glass in the act of dripping, and you get a teardrop shape with an elongated tail. All the stresses are aligned in the drop and concentrated at the tail joint. The drop body is damn near indestructible, but the slightest stress on the tail and the whole thing instantly turns to sand. Super-cool and mostly useless bit of fun material science.

This lovely YouTuber was part of the fun. (Score:2)

by BenFenner ( 981342 )

Not one of his best videos, but that just shows how good his typical videos are.

[1]https://www.youtube.com/watch?... [youtube.com]

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

if it blends (Score:2)

by Growlley ( 6732614 )

it can,

But what about my momma? (Score:1)

by sabbede ( 2678435 )

Is she or is she not too fat to pass through herself? And why has no one yet raised this question?

Re: But what about my momma? (Score:1)

by newcastlejon ( 1483695 )

Your mommaâ(TM)s so fat she outweighs the needs of the many.

Why are manhole covers round? (Score:2)

by mkwan ( 2589113 )

I wonder if there's a noperthedron equivalent of a manhole cover

Someone is speaking well of you.