First Shape Found That Can't Pass Through Itself

6 months ago

Prince Rupert of the Rhine won a bet in the late 1600s proving that a tunnel could be drilled through one cube large enough for another cube to pass through.
Mathematicians have since explored which other shapes, known as convex polyhedra, have the 'Rupert property' allowing one copy to pass through another via a straight tunnel.
For centuries, only the cube was known to have this property, but in 1968, Christoph Scriba proved the tetrahedron and octahedron also have it.
Recent research has identified many convex polyhedra with the Rupert property, leading to the conjecture that all convex polyhedra might possess it.
Jakob Steininger and Sergey Yurkevich have now discovered the 'Noperthedron,' a 90-vertex, 152-face shape that cannot pass through itself, disproving the conjecture.
The proof involved theoretical advances and extensive computer calculations, analyzing shadows cast by the shape in different orientations.
The Noperthedron's discovery relied on a mix of global and local theorems to rule out all possible orientations for a Rupert passage.
This breakthrough opens new avenues for studying shapes without the Rupert property and challenges previous assumptions in discrete geometry.

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