Lasers are awesome, but they are essentially a two-dimensional tool.
This instructable is essentially a practice piece for a simple trick* that can produce three-dimensional objects with two-dimensional cuts.
The final result is not going to fool anybody, but it does produce gems that would look fine as part of a stage or Halloween costume.
(*borrowed from Steve Crayons' Chess Pieces Instructable. You should go check it out.)
Step 1: What You Need
The diamonds are cut from 5mm clear acrylic - if you have thicker material, just re-scale the files to match.
You'll also need a way to lift the diamonds from the cut material - I used a piece of masking tape rolled inside-out to make a sticky reaching tool.
I've also attached a variety of versions of the files for you to use.
Step 2: First Cuts
The files I've created have blue and green cutting lines.
Both lines are cut right through the material, but the green should be set to cut after the blue.
You need to make sure you use your honeycomb cutting bed, or the pieces will drop out and be impossible to realign, and it's a good idea to fix your material in place to prevent annoying mis-cuts in the next step.
Run the file, and keep hold of all the parts made.
Step 3: Lift
Without shifting the material at all, lift the cut pieces out of the sheet of acrylic.
The easiest way to do this is use something sticky.
Step 4: Second Cuts
Save all the parts from the first cut as a block, turn them through 90 degrees, and lay them back into the hole they came from.
You can leave off the top layer of off-cuts, as cutting them will just generate more tiny scraps to pick up later.
Run the exact same cuts again, lift out the pieces, and there you go!
Step 5: Finishing
You may find that the tiny offcuts stick to the corners of the gems, but they come off fairly easily with a firmly-applied thumbnail.