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This is one of my favorite drills, old but going strong, thou you have to make your own drill bits...

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Sure you can drill it, but as said it's not them most cooperative material around, I've used a flat drill for pearls.
Some drill it under water or oil to dampen vibrations, I don't know how much it...

I have heard of that they did exist but sadly have no more info on it.
Amber is thermoplastic, it can be press-cast into any shape you like.