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
Pappus's hexagon theorem Pappus's hexagon theorem In mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points "A", "B", "C", and another set of collinear points "a", "b", "c", then the intersection points "X", "Y", "Z" of line pairs "Ab" and "aB", "Ac" and "aC", "Bc" and "bC" are collinear, lying on the "Pappus line". These three points are the points of intersection of the "opposite" sides of the hexagon "AbCaBc". It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem"