I was wondering the same thing. It would have to be a sphere, a thick shell constructed of an incompressible material such that the inward pressure causes compression. Some kind of honeycomb structure?

The weight of the shell depends on the area (goes up as the square of the radius). The lift depends on the volume (goes up as the cube). Seems like for a large enough size you might be able to get positive lift.

The inward pressure per square inch of shell is constant (14.7 lbs. per sq. in. at sea level with a total vacuum inside), so as long as the inward pressure is distributed evenly it doesn't seem like it has to be stronger just because it is larger.

Inside would only have to be a partial vacuum. You can heat the gas inside to reduce the pressure differential, which might not be too costly if the shell is fairly thick and provides thermal insulation. Here again the volume vs. area works in your favor.

Conclusion: Probably Buckminster Fuller could come up with something.

No, because there is no known material (even exotic stuff like nanotubes) that can hold a vacuum AND be lighter than the contained volume equivilant of air.

Some analysis on this topic has been done: https://en.wikipedia.org/wiki/Vacuum_airship#Material_constr...

If your spongy structure is capable of withstanding a half decent vacuum it will likely be much heavier than the volume of that structure filled with air.

But it would still be only marginally lighter than hydrogen or helium, and require a much more sturdy support mechanism.