Covering New Ground with Polygons

Grab a pen and draw a figure. Follow a few rules: keep your lines straight, don’t pick up your pen, don’t cross the lines, and finish at the spot where you started. You’ll have a polygon.

The biggest hexagon is 3.92% bigger than the regular hexagon. Mossinghoff
Each of these two hexagons has the same diameter, since the greatest distance between any two points is the same in each figure.