You see, at the micro level aerographite resembles a network of porous carbon tubes (pictured at right), which calls to mind the concept of the carbon nanotube. Much like the Buckminsterfullerene, this microscopic structure is predicted to be the mainstay of construction someday, just as soon as we can create nanomachines capable of erecting buildings!
And just think of it, diamonds are essentially carbon that has been layered and then super-compressed to become a near-indestructible material. If you have the ability to assemble tiny atomic structures made out of carbon, you can essentially create not only create diamonds, but also objects that are both extremely light and highly resilient. And just so you know, the researchers who produced aerographite have indicated that it can be compressed without damage.