This picture shows the structure of the Alum crystal. It looks a bit like two pyramids stuck together along one of the faces with slightly flattened tops and squared edges.

This picture also shows that as the crystal grows, if you do not pay close attention to conditions, the quality may decrease (here, milkyness increased).

To see what the effect of "contaminating" (or "doping") this crystal with chromium salts has, Click Here.