First Shape Found That Can't Pass Through Itself (quantamagazine.org) 34
Mathematicians have identified the first shape 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.
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.
Finally! (Score:5, Funny)
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We finally know how to keep Noperthedron shaped animals from using the doggie door!
Hey now! Nopey is not fat! He’s just..multi-faceted.
More explanation (Score:5, Informative)
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 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.
Re: More explanation (Score:5, Funny)
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Let Them Eat Lies!
Re:More explanation (Score:5, Informative)
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 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 here [youtube.com].
It's quite a "hole", however. There's not a lot left of the original cube.
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What if it's a cellular peptide cake with mint frosting?
Did they use AI? (Score:2)
How can you know?
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No. They worked out an algorithm that massively decreases the search space by using agressive nearness heuristics.
Also, See sig vvvvvv
Pedantic Correction (Score:4, Informative)
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See Tom7's video linked in a comment above (although I'm not sure why the OP did not name him). A sphere has too much symmetry, you cannot cut a sphere-cross section i.e; circle) in a sphere that is large enough for the sphere to pass through, while leaving enough "material" for there to still delineate the whole.
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Like a plane? Or a line? (Score:2)
Do I get two awards?
so when will we see a Rupert's cube? (Score:2)
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)
Let's try!
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Just accuse them of being LGBTQ+ and MAGAs will do it for you.
Prince Rupert's Drop (Score:5, Interesting)
This lovely YouTuber was part of the fun. (Score:2)
https://www.youtube.com/watch?... [youtube.com]
if it blends (Score:2)
But what about my momma? (Score:1)
Re: But what about my momma? (Score:1)
Why are manhole covers round? (Score:2)
I wonder if there's a noperthedron equivalent of a manhole cover
What is the definition of cannot pass through? (Score:2)
What is the definition of cannot pass through? Would the copy that is trying the pass through be blocked in some way?
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I was always under the impression that manhole covers were round for this very reason. Maybe I am missing something.
Umm? Sphere? (Score:1)
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The sphere is not a polyhedron.
Tom7's YouTube Video (Score:2)
Tom7 is a colleague of mine. He puts out a couple of entertaining videos every year about esoteric semi-comp-sci related stuff.
Here's the video referenced by the linked article where he discovered this shape:
Rupert's Snub Cube and other Math Holes [youtube.com]
What with the obvious contradiction? (Score:2)
Or
"In 1968, Christoph Scriba proved the tetrahedron and octahedron also possess this quality."