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First Shape Found That Can’t Pass Through Itself | Quanta Magazine

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Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s big enough for the other to slide through? Perhaps your instinct is to say “Surely not!” If so, you’re not alone. In the late 1600s, an unidentified person placed a bet to that effect with Prince Rupert of the Rhine. Rupert — a nephew of Charles I of England who commanded the Royalist forces in the English Civil War — spent his sunset years studying metallurgy and glassmaking in his laboratory at Windsor Castle. Rupert won the bet. The mathematician John Wallis, recounting the story in 1693, didn’t say whether Rupert wrote a proof or bored a hole through an actual cube. But Wallis himself proved mathematically that, if you drill a straight tunnel in the direction of one of the cube’s inner diagonals, it can be made wide enough to allow another cube through. It’s a tight squeeze: If you make the second cube just 4% larger, it will no longer fit. It’s natural to wonder which other shapes ha

First Shape Found That Can’t Pass Through Itself | Quanta Magazine Home First Shape Found That Can’t Pass Through Itself Read Later Share Copied! Comments Read Later Read Later geometry First Shape Found That Can’t Pass Through Itself By Erica Klarreich October 24, 2025 After more than three centuries, a geometry problem that originated with a royal bet has been solved. Read Later The Platonic solids that have six, eight, 12 and 20 sides can pass through themselves. David Renshaw Introduction By Erica Klarreich Contributing Correspondent October 24, 2025 View PDF/Print Mode combinatorics geome

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