" The maximum diameter a hexagon can have is twice its side length, and the minimum is $s\sqrt{3}$. "

The diameter of a set (by definition) is the supremum of the distances between two points of the set. --JBL 11:55, 1 November 2006 (EST)

English please? --I_like_pie 20:21, 1 November 2006 (EST)

"Supremum" = "least upper bound." In many situations this just means "maximum," but there are others where it doesn't. For example, in an open set such as the interior of a circle or radius $r$, there are no two points at a distance $2r$ from each other, but the diameter of the set is still $2r$. Or, if we consider the set $\{1, \frac12, \frac13, \ldots\}$ this set has diameter 1 even though it contains no two points at distance 1 from each other.

The point was just that there is only one value which is the diameter of a given set. The notion you're trying to capture is something to do with the lengths of paths from points on the hexagon passing through the center, or some such -- it would probably be better just to give the lengths of the apothem and circumradius, instead.

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