a cube
Sorry I don't think it makes one
no
yes ithink
Diamonds can be cut into almost any shape.
Do you mean diamonds as in diamond rings, or as in a pack of cards? If the crystal version, then you can't do anything with them other than by grinding bits off to change the shape.
Octahedron
no
As found in their natural state, any
a hexagon
All diamonds are formed from carbon.
Some raw diamonds appear to be pyramids, or a pair of pyramids joined at the base. The edges are not sharp and these descriptors only approximate the shape of the natural stone. You can follow the link, below, to learn more about raw diamonds.