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We Have Concerns

Discovering the Noperthedron

We Have Concerns

Anthony Carboni/Jeff Cannata

Pop, Society & Culture, Culture, Games, Gadgets, News, Internet, Comedy, Science

4.92K Ratings

🗓️ 2 February 2026

⏱️ 51 minutes

🧾️ Download transcript

Summary

Can one six-sided cube seamlessly pass through another of equal size? The answer may surprise you. And the quest to discover convex polyhedrons that don't behave that way is even wilder. After more than three centuries, a geometry problem that originated with a royal bet has been solved, and Jeff and Anthony lay it all out for you.

Transcript

Click on a timestamp to play from that location

0:00.0

The Tower where they murdered the boys will never lie to you.

0:17.7

This is we have concerns.

0:19.5

Hi, Jeff Kanata.

0:20.6

Hi, Anthony Carboney. Hello, Concern concerned citizens. Oh, I have a real fun topic this week. A humdinger, would you say? I believe so. It's a real humdinger. This humdinger posted by our Humdinger provider in chief, Z, Synergy Mansfield, doing that work in the discord.

0:38.4

It's a title that we're workshopping, humdinger provider-in-chief. It doesn't quite roll off

0:44.1

the tongue the way we'd like. Yeah. The sign over the door is a little lengthy. I'll be honest.

0:50.3

Yeah. Hey, if you'd like to suggest a story, you can absolutely do so. We have a we have concerns show at gmail.com. We've got a subreddit that we never check. We have social media. And if you talk to us on it, we'll scream. But the best way to do it is over in our Discord. And to join that, just head to we have concern. Patreon.com slash we have concerns. So this is a math story and it's fascinating to me.

1:14.5

It's something I've never encountered before.

1:17.3

Math?

1:18.6

Yeah.

1:19.1

What is that?

1:20.3

As an ex-actor and now house husband, I've never.

1:26.6

Never?

1:29.1

What is this math you speak of?

1:31.9

As a science podcaster, never seen it, never heard of it. I've never seen math.

1:34.2

And my hands are so soft from never doing a day of physical work.

1:38.5

That's right.

1:39.3

But my vocal cords are supple.

1:41.2

Oh, they're so warmed up.

1:44.5

Anthony, you love, you like a D&D. You like a tabletop board game. I do. I would like you to

1:51.9

imagine, if you will, two D6s, your average six-sided dye, the most conventional cube, you can imagine a six-sided die? The way you're describing them already makes me feel like you've loaded them and you're cheating. And I know there aren't even real dye. And I know it's not even about that. Completely normal. You can weigh them in your hands. You can see they're totally... You can count the sides with me. One, two, three, four, five, six. Only six.

2:18.3

Everything is possible with the...

...

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