Hexagon circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. If the successive sides of a cyclic hexagon are "a", "b", "c", "d", "e", "f", then the three main diagonals intersect in a single point if and only if . If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent. If a hexagon has vertices
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