Okay, so these are what came out of my failed first attempt at the previously mentioned Cool Model (CM). I wanted to explore the differences in how the modules locked together in the standard versus the inverted configuration - the CM is mostly composed of the inverted type. I think the holes where the vertices meet is pretty darn telling -- this thing really wants to slide apart. Just picking it up, you can feel how squishy it is. The standard model, on the right, is a much more solid piece.
What does this mean? Paper being what it is, especially slightly glossy paper like this, it really wants to unbend. Just a little, but it's enough to make the tabs attempt to twist out of the pockets on the inverted model, where it actually helps shove the tabs into the standard pockets. It's less pronounced on the more standard origami paper I tested, but still there. Therefore, I think I'm going to go ahead and make a modified version of the CM for now, using standard modules instead of inverted for the hexagonal faces. It will look different, but it should be equally cool in its own way. I just need to decide on colors -- I've re-purposed all the original squares into these two models and a flower ball that I'm still working on! :D
(closer views of each model are in my Flickr account)