Tangential quadrilateral all of whose sides are tangent to a single conic section has three diagonals that meet at a point. From a tangential quadrilateral, one can form a hexagon with two 180° angles, by placing two new vertices at two opposite points of tangency; all six of the sides of this hexagon lie on lines tangent to the inscribed circle, so its diagonals meet at a point. But two of these diagonals are the same as the diagonals of the tangential quadrilateral, and the third diagonal of the hexagon is the line through two opposite points of tangency. Repeating this same
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