The property is (was) specific to convex polyhedrons.

Thats my confusion too, there's even a "sphere" (polygon with enough sides to be sphere like) image in the article.

Everything goes in the square hole.

Haha same. First thought was: Have they actually ruined it even more?

new bestagon just dropped

I always liked how the Borg's algorithm to assess nonsense shapes is to throw more Borgs at it instead of being like "Further data is required" and then return to the area where the data was collected. If they couldn't collect it, then run a diagnostic on the Borg that presented it. It's almost like the Borg collective never assimilated any species that had hackers or social engineers in their populations.

New kind of sewer cover? Shrugs.

I am not a math expert; I never even took calculus. From reading the article, originally the question three centuries ago was whether or not a cube could be rotated in such a way that another identically sized cube could pass through it (like if a tunnel was cut in it). The answer turned out to be yes, although it’s very close. Then as mathematicians started investigating other shapes the answer kept being yes. Eventually the question became, “are there any shapes that can’t pass through themselves?” It’s hard to prove because there are so many angles that have to be checked. Recently mathematicians were able to prove that if you can rule out one angle, you can also then rule out a certain (varying) percentage of adjacent angles. Using that makes it easier to rule out more rotations and they’ve now found the first shape where they can definitively say it can’t pass through itself.

That's a physics question, not a maths question :)

The property is (was) specific to convex polyhedrons.