The flat Lap is the best tool that I've found for grinding down a surface such as a thin plate or small thunder egg. Larger rocks like bookends can be done with this method, but the Vibralap is a lot more efficient for big stuff.
The video at left demonstrates how I made my own lap machine out of a few spare parts. You can but these, of course, but to get one that has both the torque you need to put pressure on a diamond plate, then plan on paying plenty.
I first used silicon carbide paper glued to wooden rounds for my grit. The 120/240 wore out quickly. That was the first plate I replaced with a 12" diamond round. Now I have all diamond plates that attach with velcro to the steel drive:
80/100/180/240/300/400/600/1000.
Typically, I use the 80 to square things up and grind down dimensions of rocks. The progression of grinding for most rocks is 100/240/400/600. For very hard agates I will add the 180/300 and 1000 discs to the process.
Below is a sketch of the lapper.