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 12. The cube and octahedron (same as triangular antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular, uniform and dual polyhedra and polytopes, shown in these skew orthogonal projections: A "principal diagonal" of a hexagon is a diagonal which divides the hexagon into quadrilaterals. In any convex equilateral hexagon (one with all sides equal) with common side "a", there exists a principal diagonal "d" such that and a principal diagonal "d" such that There is no Platonic solid made of only regular hexagons, because the hexagons tessellate, not