Saturn's hexagon change in season. These changes were observed by the Cassini spacecraft. One hypothesis, developed at Oxford University, is that the hexagon forms where there is a steep latitudinal gradient in the speed of the atmospheric winds in Saturn's atmosphere. Similar regular shapes were created in the laboratory when a circular tank of liquid was rotated at different speeds at its centre and periphery. The most common shape was six sided, but shapes with three to eight sides were also produced. The shapes form in an area of turbulent flow between the two different rotating fluid bodies with dissimilar speeds. A
Hexagon formula_7 of its circumscribed circle. If a regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on the circumscribing circle between B and C, then . The "regular hexagon" has Dih symmetry, order 12. There are 3 dihedral subgroups: Dih, Dih, and Dih, and 4 cyclic subgroups: Z, Z, Z, and Z. These symmetries express 9 distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order. r12 is full symmetry, and a1 is no symmetry. p6, an isogonal hexagon constructed by three mirrors can alternate long