There is a difference between hardness and toughness. A hard (strong) object requires a lot of force to break it but it WILL break. A tough object deforms without breaking. An object can indeed be both hard and tough, but diamond is only hard. Also, diamonds (any crystal really) are easy to cut along their shear planes, which are defined by the lattice structure of the crystal. A diamond can also be ground down abrasively by materials softer than itself, this happens by knocking off high points sticking out from the surface of the diamond (which are weaker because they are sticking out). Furthermore, you can polish a diamond using fire, essentially burning off the surface of the diamond, which is just a form of carbon after all.
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