I believe you're talking about a kinematic mount. (The three points are at 120 degrees.) The main advantage of a kinematic mount is that it allows for expansion/contraction without the center changing position. It also requires a fair amount of preload so the balls don't walk out of the grooves.
While it is true that anything with more than 3 legs is "over constrained" it can also be more stable. (Ever sat on a 3 legged stool?) I'd suggest you just want something heavy and sturdy with four legs and height adjustable feet so that you can level it. (A good test would be to sit on the table and wiggle around. If the table "feels" solid, you're probably good.) Bolt the machine to the table top and you should be good to go.


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