If Bucky Fuller designed a bike, it might look something like this idea from Romanian industrial designer Ionut Predescu. He calls it a Tensegrity frame, a term invented by Bucky and a portmanteau of Tensional Integrity. Cables are incredibly strong in tension and useless in compression, so Predescu has replaced tubes and welded connections with far lighter wires. There doesn't even have to be a rigid connection between the seat post and the horizontal element, the wires do it all.
High strength tensegrity frame made of carbon fiber and kevlar cables. A balance between compression and tension elements is able to offer a lighter alternative to traditional bike frames by producing a stiff structure where elements seem to float one against the other.