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
Heesch's problem a tile may be surrounded, its Heesch number is said to be infinite. In this case, an argument based on Kőnig's lemma can be used to show that there exists a tessellation of the whole plane by congruent copies of the tile. Consider the non-convex polygon "P" shown in the figure to the right, which is formed from a regular hexagon by adding projections on two of its sides and matching indentations on three sides. The figure shows a tessellation consisting of 61 copies of "P", one large infinite region, and four small diamond-shaped polygons within the fourth layer. The