Inspired by the previous posts, I bought a few different types of sandpaper and tried folding a simple tessellation out of them. Unfortunately, the result is that none of these papers was suitable even for a very simple model.
One important characteristic of sandpaper is how coarse the grain is and the other what kind of backing material is used to hold the abrasive layer (usually paper or cloth). Two different grains of paper-backed sand paper tore very easily across the crease lines as I tried to precrease a 16×16 grid from a 23 cm sheet. The result was a bit better if I folded the line as a valley first and then as valley (looking from the abrasive layer’s side) than the other way around. Still, I wasn’t even able to finish the grid before papers tore.
I had better hopes for the cloth-backed sandpaper and initially I thought I was going to succeed after I made the first few folds in one direction. But then I made a single crease in the perpendicular direction and the paper just tore off along almost the whole length. Actually, it felt more as if it broke rather than tore.
I think the main issue is that the abrasive layer is completely brittle, so making a sharp crease just breaks rather than bends it, and then then comes the fact that it consists of sharp-edged grains which pierce through the backing paper or cloth when a valley fold is made. If only mountain folds were needed, I think there would not be so much tearing. But you can only get so far with mountain folds alone.