A single bubble can be 1 meter in earth gravity, 100 kilometer in low earth orbit or 1000 kilometers in deep space. Foams made of many bubbles could be far larger in size.
NOTE: the size of a 1000 kilometer bubble is nearly the size of Charon, the moon of Pluto. Charon is 1200 kilometers in diameter. Saturn’s moon Tethys is 1050-1080 kilometers in diameter Ceres the largest object in the asteroid belt is 970 kilometers in diameter. A single tesselation foam (like in the picture) of 1000 kilometer bubbles would be about the size of Earth’s moon. A Penrose tesselation like the one in the picture of 1000 kilometer bubbles would be in between the size of Neptune or Saturn. A Tesselation foam of 100 kilometer bubbles in earth orbit could form an object the size our existing moon or larger.
Metal can be evaporated to coat the inside of the bubble for reflective sails and telescopes.
Large structures can make telescopes that are millions of times more powerful than the Hubble Space telescope and solar sails that are light weight and fast.
Extreme Expeditionary Architecture: Lightweight Lunar RVs that can be connected into a larger mobile base camp. Let 8 move around many miles and explore a lot of the moon. the two RV’s could be deployed in one launch payload.
Hopefully NASA’s Innovative Partnership program can pick up where the Nasa Institute for Advanced Concepts left off and continue this kind of innovative work.
Further reading on space propulsion and colonization on advancednano: