The hexagon at Saturn's north pole

"Geometric whirlpools" are discussed in a Nature article:

Researchers at the Technical University of Denmark in Lyngby have created similar geometric shapes (holes in the form of stars, squares, pentagons and hexagons) in whirlpools of water in a cylindrical bucket. The shapes appear easily enough once the bucket is spinning at a rate of one to seven revolutions per second, they say.

But the researchers admit their studies may not be relevant to planetary-sized systems.