In a breakthrough announced in October 2025, mathematicians Jakob Steininger and Sergey Yurkevich discovered the first shape proven to lack the “Rupert property” - meaning it cannot have a straight tunnel bored through it large enough for an identical copy to pass through[1].
Named the “Noperthedron,” this 90-vertex, 152-face shape disproved a centuries-old conjecture that all convex polyhedra would have this pass-through property, first demonstrated by Prince Rupert with a cube in the 1600s[1:1].
The proof combined theoretical advances with massive computer calculations, examining approximately 18 million possible orientations. “It’s a miracle that it works,” said Steininger, who developed the proof with Yurkevich while both worked in Austria[1:2].
This resolved a geometry problem dating back to Prince Rupert’s royal bet that one cube couldn’t pass through another. While Rupert won that bet, and mathematicians later proved many complex shapes could have pass-through tunnels, the Noperthedron finally provided the first counterexample[1:3].
I’m not sure about it, but I think that a sphere is such a shape by default and the shape found is an aproximate sphere. So I don’t really understand where are the problem.
The property is (was) specific to convex polyhedrons.
It works for shapes that are also pretty close to a sphere. It works for a soccer ball and for a D120. This is the first counter example found.
The problem applies specifically to polyhedra. The shape found (“Noperthedron”) is fundamentally different from a sphere. And, anyways, the sphere is not such a shape… i.e. it’s essentially impossible to pierce a tunnel in a sphere which would accomodate for another sphere with the same or higher diameter.
“Essentially” in the sense of “fundamentally”, not the colloquial “nearly”, yes. By definition, a sphere is identical no matter how you rotate it, so its projection into 2D space does not change.
Thats my confusion too, there’s even a “sphere” (polygon with enough sides to be sphere like) image in the article.