The Shape That Can’t Pass Through Itself
The Quanta Podcast
Quanta Magazine
4.7 • 638 Ratings
🗓️ 13 January 2026
⏱️ 27 minutes
🧾️ Download transcript
Summary
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.
Transcript
Click on a timestamp to play from that location
| 0:00.0 | Have you ever had the urge to sneak behind the cordoned off areas of a museum? |
| 0:05.7 | Or roam the halls after closing time? |
| 0:08.7 | The Smithsonian's flagship podcast, Side Door, will sneak you behind the scenes of the world's |
| 0:14.5 | largest museum and research complex. |
| 0:17.5 | Come learn about the ghosts that supposedly walk the museum halls after dark. |
| 0:21.6 | How a train robbery gave rise to criminal forensics, |
| 0:24.6 | why leeches are actually the coolest thing ever, and how to get away with murder in the Arctic. |
| 0:30.6 | Maybe. |
| 0:31.6 | You'll discover stories of history, science, art, and culture you won't find in a display case. |
| 0:43.5 | You can listen to Side Door wherever you get your podcasts, or find us online at s.edu. Slidedoor. |
| 0:49.0 | One of the lovely things about math is that it's full of these problems that are simple to state but conceal great puzzling depth. |
| 1:03.1 | Take the famous colats conjecture. |
| 1:05.5 | You can start with any positive integer, 10 or 71 or 1,635,132. |
| 1:15.3 | And if it's even, you divide it by two. |
| 1:18.0 | If it's odd, you multiply it by three and add one. |
| 1:21.5 | And you do that over and over again. |
| 1:23.8 | For every number that has ever been tested, up to extremely big ones, it always eventually |
| 1:30.3 | ends up at one. Try it yourself. It'll work. But that doesn't make it mathematically true. |
| 1:36.3 | No proof exists that shows that this is true for all possible integers, and it would take some |
| 1:41.8 | kind of great mathematical innovation for that to happen. |
| 1:45.8 | We don't have a counter example, but we can't show that one doesn't exist. |
| 1:51.3 | It's a form we've seen before, and we'll see again, simple to state seemingly true, |
... |
Please login to see the full transcript.
Disclaimer: The podcast and artwork embedded on this page are from Quanta Magazine, and are the property of its owner and not affiliated with or endorsed by Tapesearch.
Generated transcripts are the property of Quanta Magazine and are distributed freely under the Fair Use doctrine. Transcripts generated by Tapesearch are not guaranteed to be accurate.
Copyright © Tapesearch 2026.