Hexagon has no degrees of freedom but can seen as directed edges. Hexagons of symmetry g2, i4, and r12, as parallelogons can tessellate the Euclidean plane by translation. Other hexagon shapes can tile the plane with different orientations. The 6 roots of the simple Lie group , represented by a Dynkin diagram , are in a regular hexagonal pattern. The two simple roots have a 120° angle between them. The 12 roots of the Exceptional Lie group G2, represented by a Dynkin diagram are also in a hexagonal pattern. The two simple roots of two lengths have a 150° angle between
Saturn's hexagon Saturn's hexagon Saturn's hexagon is a persisting hexagonal cloud pattern around the north pole of Saturn, located at about 78°N. The sides of the hexagon are about long, which is more than the diameter of Earth (about ). The hexagon may be a bit greater than wide, may be high, and may be a jet stream made of atmospheric gases moving at . It rotates with a period of , the same period as Saturn's radio emissions from its interior. The hexagon does not shift in longitude like other clouds in the visible atmosphere. Saturn's hexagon was discovered during the