I've run into a snag when modelling a polyplane mesh. Here's how the model looks like:



As you can see, the cube is made up of polyplanes of different colors. I choose this way of modelling since I'm doing a Maya Vector render for Flash. Now I am trying to find a way to get more round edges, but I just can't seem to find a good way of doing it.
I've tried Combine and then Smooth, but each former polyplane in the mesh is still treated as an individual plane and get smoothed this way:

That happens even if I choose Delete by type > History. I of course figured that it wouldn't be that easy making the the corners of the cube smoother, but I had to try.

So, any suggestions?