Looking at the Wellington cutaway, it is a lattice, two-dimensional in some areas and curved into a cylinder in others. Neither is truly geodesic in the sense of being a self-defining surface of linked rods. It is only in two-way curved surfaces that the geodesic structure becomes rigid.
The added rigidity in the Wellington comes from having a very thick skin, anyone with mechanical knowledge will recognise
(bd^3)/12
which is the moment of inertia of a beam of width b and depth d, the stiffness being proportional to the cube of d.
In the context of a lattice structure Bearfoil is quite correct in drawing a parallel with honeycomb materials where the separated skins provide the stiffness and the honeycomb simply defines the gap between skins.
PS - Apologies for lapsing into lecturer mode, will try not to in future!