Lots of projects use LEDs. Here we'll be modifying the LED itself to resemble a gem. Doing this also changes the light output pattern of the LED, throwing more light to the sides and less forward.
Step 1: The Inside of the LED / the Plan
The common LED has a die (the light emitting element) in a cup on one lead, and a fine wire from the other lead to the die, all enclosed in plastic. This plastic enclosure protects the sensitive electronic elements and focuses the light produced. So long as we don't get too close to the delicate parts inside we can safely reshape the lens.
Step 2: Materials and Tools
The LED. I'm using a superbright white in a clear package. Other low power LEDs should work fine. High power LEDs have a different construction and probably won't work here.
Pliers. Something to hold the LED.
File or sandpaper block. To shape the plastic lense.
Lapping Block. A solid block covered in cloth to polish up the facets on the reshaped LED. I've also had success with smooth ceramic tiles.
Step 3: Shaping, Part 1
Taking the LED in the plier by the leads, work two sides of the LED against the file or sandpaper block to grind down the lens to a wedge.
Step 4: Shaping, Part 2
Grind down the other 2 sides of the LED to make a pyramid.
Step 5: Polishing
Rub the facets against the lapping block to work out the scratches left by the shaping process. A little oil or polishing rouge may help here. If you shaped with a good file or fine sandpaper this should go fairly fast. if you shaped with course sandpaper it may take longer. If your experiments find a better method for this, please drop a comment.