"The Diamond Theorem" -- see below -- is described as "... finite projective geometry," showing the number of permutations possible in "... the four-diamond figure as a 4x4 array of two-colour, diagnnally-divided squares."
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About 20% of all diamonds mined are gem-quality diamonds.
You may be thinking of gemstones and industrial diamonds. Gemstones represent about 20% of all diamonds mined, and the remainder is industrial diamonds.
Yes, diamonds can cut glass, because diamonds are harder than glass.
The plural possessive is diamonds'.
a diamonds cleavage is the cleavage of a diamond