I did a few experiments with cork in the style of Matakishi's generic desert buildings, just to see how well it would work with the cheapo cork tiles you can get in Wal-Mart and Michaels. The first thing I found out is that the tiles you can buy at Michaels for US$10 per pack of four appear identical to the ones you can buy at Wal-Mart for $5 a pack. The tiles shown here I bought at a drugstore for about $5 a pack; they're the same brand as the ones at Wal-Mart, and appear to be identical, but the packaging is slightly different. Once I'm done with these four tiles I'll open up the one from Wal-Mart and see if there's a difference in how they cut.
The cork cut very easily, easier than foamcore. For the windows and doors I cut all the way through the cork, going from a corner to the center of that edge. 8 cuts per window, but it went quickly because I made all the "down" cuts on the sheet at once, then turned the sheet 90 degrees and made all the "left" cuts. And so on, until I'd turned the sheet full circle and could pop out the scrap from the windows. To make the long exterior cuts, I made three passes much like I would with foamcore. If I tried to cut all the way through in one pass it would tear out pieces of the cork, but using several light cuts resulted in smooth, clean edges. There was some mess, tiny (0.1mm or so) bits of cork that came free when I popped the windows out, but there's no visible effect on the edges.
I glued most of it together with superglue. A lot of superglue. Surprisingly, I only glued myself to the superglue tube once. Some parts were glued together with wood glue instead; they both work, but the superglue dries much faster, letting me assemble the pieces in much less time.
Matchsticks (from Michaels) provided the windowsills and ledges for the drop-in ceiling. The cork is 5mm thick; I glued lugs to the bottom of the second floor about 6mm in from the edges to help center it on the bottom floor. It goes on and off easily, while the roof takes some fiddling to set into place properly.
The base is a piece of compressed paper board that I got at Michaels. It's basically the same material as the back of a clipboard, and if I can find a supply of cheap clipboards I'll use them instead. I guess it's time to visit the dollar store again.