Some time ago, I realized that the CBP can be tesselated. I made a series of 4 pieces, starting with the original CBP and then folding 4, 9 and 16 CBPs from one piece piece of paper. This is the fourth model in this series.
Peter Budai of Hungary has also found out that the CBP can be tesselated. He says that he made this discovery in 1996, some time before I did.