Hi Mark, so as mentioned in that discussion Steve linked to, you can get something very close to a super ellipse by making a shape out of hyperbola segments.

To do that, first draw a square like this:



Then use the Conic command under Draw curve > More > Conic, and snap the first 2 points on to the midpoints and the apex point on to the corner and pick a point inside to make a hyperbola segment like this:



Now that can be mirrored to produce the full shape:




- Michael