Hexagon of the circumscribed circle, which equals formula_1 times the apothem (radius of the inscribed circle). All internal angles are 120 degrees. A regular hexagon has 6 rotational symmetries ("rotational symmetry of order six") and 6 reflection symmetries ("six lines of symmetry"), making up the dihedral group D. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be
Equilateral polygon if and only if the alternate angles are equal (that is, angles 1, 3, 5, ... are equal and angles 2, 4, ... are equal). Thus if the number of sides "n" is odd, a tangential polygon is equilateral if and only if it is regular. Viviani's theorem generalizes to equilateral polygons: The sum of the perpendicular distances from an interior point to the sides of an equilateral polygon is independent of the location of the interior point. The "principal diagonals" of a hexagon each divide the hexagon into quadrilaterals. In any convex equilateral hexagon with common side "a", there