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
Hexagon formula_7 of its circumscribed circle. If a regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on the circumscribing circle between B and C, then . The "regular hexagon" has Dih symmetry, order 12. There are 3 dihedral subgroups: Dih, Dih, and Dih, and 4 cyclic subgroups: Z, Z, Z, and Z. These symmetries express 9 distinct symmetries of a regular hexagon. John Conway labels these by a letter and group order. r12 is full symmetry, and a1 is no symmetry. p6, an isogonal hexagon constructed by three mirrors can alternate long