The Quanta Podcast The Shape That Can’t Pass Through Itself
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Jan 13, 2026 Erica Klarich, a science and math writer and longtime Quanta contributor, dives into the intriguing world of geometry. She discusses the Noperthedron, a groundbreaking discovery that challenges the Rupert tunnel conjecture, revealing a shape that cannot pass through itself. Klarich explains the historical context behind the puzzle, the complex characteristics of the Noperthedron, and the creative use of computer searches in its discovery. She also touches on the implications for geometry and recommends Jane Austen's Emma as a literary delight.
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Prince Rupert's Dice Bet
- Prince Rupert imagined and bet that a cube could be tunneled so an identical cube could pass through it.
- That historical bet launched the long study of “Rupert tunnels” in geometry.
Orientation Changes What Shapes Fit
- A cube's silhouette depends on orientation and can form a hexagon when viewed from a corner.
- That hexagonal projection can contain a face-square, enabling a same-size cube to pass through.
Rupert Tunnels And The Conjecture
- Rupert tunnels generalize the cube trick to convex polyhedra: one copy passes through another of the same shape.
- Mathematicians observed many shapes allow such tunnels, prompting a conjecture that all convex polyhedra might be Rupert.
