What are the pro/cons of polyhedral cranked wings? Dihedral wings seems to be very common (almost if not all low-wing airliners, many modern gliders,...). Polyhedral seems to be less common and mainly found in relatively old aircraft (F4 Phatom, F4U Corsair, DR400,...). By polyhedral, I mean at least 2 dihedral angle with a sharp discontinuity between both. I don't include wings whose diheadral angle varies smoothly along the wingspan (such as this B787).

But I was surprised to discover that this design (polyhedral with sharp angle between the distinct diheadral sections of the wing) was elected in at least 2 project whose first flight was in the last 10 years (namely the solar impulse and the qinetiq zephyr). I do realize that both examples I gave have similar missions (stay airborne as long as possible, and thus fly slowly; gather as many sun-energy as possible, and thus fly as horizontally as possible) and may thus have similar design.

Given recently-designed aircraft with polyhedral wing exist, what are the pro/cons of such design over well spread dihedral wings and over the smoothly varying dihedral angle?

EDIT: note that the polyhedral does not necesseraly increase the dihedral angle as we go away from the wing root (Be 12, Habicht,...)
While dihedral wings offer increased stability in the roll axis, they also decrease the lift that the wings provide. A polyhedral wing provides a compromise: a steep dihedral at the tip of the wing in order to maximize stability, and a shallower dihedral angle closer to the root in order to maximize lift. 


Therefore, a polyhedral wing allows the best of both worlds for a wing design. Other applications of a polyhedral wing are utilitarian; the gull wing on the Vaught F4U Corsair is designed so that the landing gear is positioned close to the ground while maintaining roll stability and aerodynamics.