The Shape That Can’t Pass Through Itself

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? It is — but what about other shapes? In a paper posted online in August, two researchers describe a shape with 90 vertices and 152 faces that they’ve named the Noperthedron, the first convex polyhedron that definitely cannot pass through itself. In this episode, Quanta contributor Erica Klarriech tells host Samir Patel about how the researchers discovered the shape, and how it solves a centuries-old geometric mystery. Audio coda courtesy of the Gemsmen Renaissance Consort.