In any good knife shop in Japan you'll see many smaller, odd-shaped stones for sale. It's quite common to use smaller triangular, square, or completely random sized pieces of stone. If you go to the old mines in Arashiyama, Kyoto Japan, and buy directly from the families that own them, this is what they are selling now that the commercial production has stopped. In the West we are accustomed to only seeing the nicely shaped rectangular stones being sold, and forget that it's not the shape of the stone that makes it work, it's the grit size. If your stone breaks in half, just modify your sharpening stroke. That's what Japan's 'Master Sharpeners' do.
Stitchawl