All of the nanotubes used in the design are as short as they can be. This gives the maximum strength. But suppose strength is not the most important attribute you are looking for and you want something even lighter (to build, for example, a dyson sphere).

If we lengthen the nanotubes, we can significantly reduce the mass without significantly reducing the strength. If we also lengthen the arms of the nanojacks, we can reduce the mass even further. (This is analogous to the length of cranes compared to their width, which is on the order of a hundred to one.)

If we increase the length by 10%, the mass is reduced by a factor of about 5. If we increase the length by 20%, its reduced by a factor of about 22. If we increase the length by 50%, its by nearly a thousand. (Of course we cannot increase the length by an arbitrary percentage, as we are constrained by how the structure fits together.)

How much the increase in length reduces the strength of the structure is unknown at this time. Along with the reduction in strength comes increasing flexibility.

In summary, this version of Buckymesh is an extremely light material, although not as strong. Let's call this modification Ultralight Buckymesh. It can be applied to either of the two versions of Buckymesh. It can also be applied to any (or any combination) of the scales of Fractal Buckymesh (e.g. by increasing the length of the arms of the super-nanojacks, but leaving the nanojacks as is).