They may be hard, but they're also brittle. Just as porcelain is actually very hard, but you know what will happen if you drop a porcelain plate on a tiled floor! (A dropped diamond can also shatter). It's fortunate that, in the cutting, diamonds have cleavage planes, as decribed in Chris's link.
Excellent proggy, apart form a couple of people there , the whole of the "invited" audience were totally and utterley lost within minutes.
From the second he started about the double slit experiment that was it by the time hed got to atoms, electrons, energy levels, exclusion theories and Quantum theories they might as well not have been there.
The vast majority of that audience now understand that they dont understand 99.99% of what he was talking about.