For a class project, nine mechanical engineering majors at Yale built a bicycle with a spokeless back wheel. One of them, redditor zhoalander, described the design in a thread at reddit:
It's a single speed setup. We used two cranks and two bottom brackets in the front to gear up the ratio. It goes from (IIRC) 53 to a 13, which is connected to the second crank and another 53 which connects to the rear hub. The rear hub is just a normal ratcheting rear hub that we mated to our belt pulley. Not sure if all these bike terms are right, but that's the general idea.
The front wheel would be almost exactly the same as the rear wheel except that it could be a little lighter. Some of the aluminum can be shaved off since there's no powertrain to connect to.
At the top of the thread, there are imgur links to more pictures of the bike.
Link via CrunchGear