English: The conjugate dual process of dissecting a regular hexagon into six congruent equilateral triangles with the same side length. Here, from six radial lines emanating from a vertex of degree 6, a regular hexagon of side length 1/(2*sqrt(3)) is insetted, along with external branches agreeing with the original radial lines. The dissection is in black, with the original radial lines orange. The dissection lines are minimally extended, such that the entire figure must be included in any corresponding inset.