Roundest Regular Solid

It is an interesting fact, but I don't think it's news. This is a blog from some guy reporting what is probably a very old thing. (And he's repeating a tweet.)

It's notable that "round" here is a particular kind of roundness. It's not compactness or deviation from circularity. It's how "pointy" it is, measured by the angle formed when you balance it on a vertex.

It's interesting that by that metric, a 12-sided figure is rounder than a 20 sided figure, which is rounder by other metrics. But it's not news.

A conjecture both deep and profound

Is whether the circle is round.

In a paper of Erdös

Written in Kurdish

A counterexample is found.

Leo Moser in Handbook of Combinatorics, Elsevier, 1995