I've been playing with Lego again recently, since Alexander enjoys it and wants me to help. He has three sorts - the normal Lego bricks, the double-size Duplo bricks and the quadruple-size Quattro bricks. The Lego bricks are not directly compatible with the Quattro bricks but the Duplo bricks are compatible with both and can be used as an interface. This allows one to create models that are very large (using the Quattro bricks) but also detailed (with the Duplo and Lego bricks).
This leads one to wonder whether a fourth size of brick would be possible, with a size half that of normal Lego bricks. It would not be directly compatible with Duplo or Quattro, but would be compatible with Lego bricks in just the same way that Lego bricks are compatible with Duplo bricks.
This is not always possible, since the "bumps" in Duplo and Quattro bricks have indentations in them which are necessary for compatibility. Most Lego bricks don't have these. But some (particularly Technic Lego) do. This leads me to wonder if the Lego company at one point planned to make such half-size bricks. I'm guessing the reason they didn't was that the pieces would be too fiddly for most fingers, too easily lost/swallowed and too difficult to manufacture with the required accuracy (the edges might also have to be dangerously sharp in order to join properly).
The Lego company did actually make a smaller version of Lego called Modulex but the bricks are 5/8 size rather than half size and are therefore not compatible.