C20⊗C20⊗C20 with g=(1,1): C15920 (Ih)
It is clearer to see when there are only two adjacent nodes:
I would say this is not unbeadable. However, as mentioned, one has to make sure the structure is strong enough to hold itself up. In my experience the best shot is to go with 3mm plastic beads and 0.4mm fish lines, which I'm currently using for the construction of a C60⊗C60 superfullerene. Other possibilities are icosahedron⊗icosahedron⊗C60 or cube⊗cube⊗C60, but I think they are not as representative and illuminating as this one.