<P> A regular hexagon has Schläfli symbol (6) and can also be constructed as a truncated equilateral triangle, t (3), which alternates two types of edges . </P> <P> A regular hexagon is defined as a hexagon that is both equilateral and equiangular . It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). </P> <P> The common length of the sides equals the radius of the circumscribed circle, which equals 2 3 (\ displaystyle (\ tfrac (2) (\ sqrt (3)))) 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 partitioned into six equilateral triangles . </P> <P> Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations . The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials . The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons . It is not usually considered a triambus, although it is equilateral . </P>

How many lines of symmetry does hexagon have