Genus-2 fullerene with local hexagonal symmetry

Chuang recently made this beaded molecule which is basically consisted of two rings fused together along their common C2 rotational axes. In the inner side of this molecule, Chuang used octagons to create negative curvatures. According to the Euler theorem, in the outer region with positive Gaussian curvature, one has to use the same number of squares for a simple torus. But here the two squares located the connected region has to be fused into an octagon in order to simulate the negative curvature in that region.
So here we need an extra two octagons in the outer side of this molecule.

Sculpture of C60 at Chem. Dept. of TKU