  The first truly non-MHV interaction vertices in the light-cone formulation of
pure gravity appear at order 6. From a closed form expression, for gravitation
in the light-cone gauge, we extract and present all 6-point interaction
vertices. We invoke symmetry arguments to explain the structure of these
vertices. Symmetry considerations also allow us to place constraints on the
structure of all even- and odd-point vertices in the theory. The origin of MHV
vertices within this formalism is also discussed.
