Later last night I finished the coding of the "real" Schwarzite D-Surface Graphenoid generation, which is done by finding the dual lattice of the following infinitely extending deltahedron:
Which is copied from Ken Brakke's site, who is the author of Surface Evolver. And his TPMS gallery always gives me a great deal of help when doing the coding of negative-curved graphenoid.
The dual of this deltahedron is then the Schwarzite D-surface graphenoid with minimal number of atoms per unit cell. (There are 8 unit cells in the figure!)
A view from high symmetric point:
Here I also present some figs of the second smaller one:
One with four unit cells: