Imagine a tube or sandwiched wall of carbon, with width W. Now fill its interior with connected buckyballs of random diameters d up to d~(Wrbuckminsterfullerene)1/2. This artificial organic structure mimics that of natural wood, bone or pumice. It retains maximum strength and rigidity with relative ease of construction (utilizing random buckyballs). This "buckyfoam" could eventually be applied where most rigid foams and many solid forms are now used, with increase in strength/mass by over tenfold. For instance, the I-beam or other superstructures might be replaced by carbon tubes suffused with buckyfoam.