The votes in favor of trivalent vertices having zero volume kept piling up. Finally Smolin noticed that he and Rovelli had made a sign mistake. This is incredibly easy to do, since there are lots of tricky sign conventions in spin network theory. Rovelli and Smolin got pretty depressed about this for a while, but I tried to reassure them that only people who write really interesting papers ever get anybody to find the mistakes. So perhaps we know a little more about the meaning of volume in a quantum theory of spacetime.
Spin networks are very beautiful and simple things.
This is because the loop representation follows Dirac's general philosophy of quantizing systems with constraints, with some extra twists here and there. When you follow Dirac's procedure for quantizing the equations what you do is this. Spin networks form an orthonormal basis of this Hilbert space. All the stuff about area and volume operators above refers to operators on this space. Then, however, you need to deal with the constraints.