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.LInk to the story: https://www.quantamagazine.org/first-shape-found-that-cant-pass-through-itself-20251024/Support the show and get bonus episodes, videos, Discord community access and more! http://patreon.com/wehaveconcernsJeff on Blue Sky: https://bsky.app/profile/jeffcannata.bsky.socialAnthony on Blue Sky: https://bsky.app/profile/acarboni.bsky.social