I don't have any particularly profound thoughts about the hexagon on Saturn (though hexagons are not unknown to nature, even if not on this scale), but Alan Henderson does.

The figure doesn't appear concentric, so whatever's causing it seems to limit the phenomenon to the boundary region. So the question (in my amateur mind) is whether the most important activity is along the sides or at the vertices--i.e., six standing waves continuously crashing into each other, or six radial "spoke" phenomena distorting an otherwise circular formation? The straight lines are a bit puzzling, though, since you'd imagine either scenario would curve the sides inward.

It would be interesting to see more area around this picture. You can excite hexigonal nodes on a spherical closed surface. I seem to remember once upon a time that this type of pattern was observed for a time on the sun.

hogland has pictures that show "ilaptus" {misspelled} is hex shaped saw that on enterprisemission.com in 2005. Very intersting.