First Shape Found That Can’t Pass Through Itself
SMRTR summary
Two teenage friends who met at math competitions just shattered a centuries-old assumption about geometry, proving that not every shape can have a tunnel drilled through it wide enough for an identical shape to pass through.
The puzzle began in the 1690s when Prince Rupert of the Rhine won a bet by proving you could bore a hole through one cube large enough for another cube to slide through. For over 300 years, mathematicians found this "Rupert property" in shape after shape, leading them to believe all convex polyhedra possessed it.
Jakob Steininger and Sergey Yurkevich, now working outside academia, created something called the Noperthedron — a 90-vertex crystal-like shape that definitively cannot accommodate a tunnel for its twin. Their proof required dividing 18 million possible orientations and testing each one through massive computer calculations.
"It's a miracle that it works," Steininger said of their delicate mathematical proof.
The discovery overturns what researcher Joseph O'Rourke called "the natural conjecture," proving that some geometric shapes simply cannot make room for themselves.
SMRTR provides this summary for quick context. The original article belongs to Quanta Magazine.
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