Hexagon is less perimeter-efficient than a square? I am confused why a hexagon seems to have a less efficient perimeter than a square. For example, given a circle and square of the same area, the circle will have a smaller perimeter.
For a hexagon, however, of side s and a square of side q both having the same area the relationship between s and q is $$q=\sqrt{\frac{3 \sqrt{3}}{2}} s\approx 1.456 s$$
Which means the perimeter of the square is 5.824s, i.e., less than the perimeter of the hexagon 6s. Is my calculation wrong or are hexagons less perimeter-efficient than squares? Wait a minute, bees can't be wrong!

I get $\sqrt{\frac {3\sqrt 3}2}\approx 1.612$ from Alpha so the perimeter of the square is about $6.448$, greater than the hexagon
