Omnidirectional Wheels-3 or 4?

I have a question regarding the number of main wheels used for the omnidrectional wheel design. (note that I consider the Mecanum wheels
to be a style of the same wheel)
I've seen some robots which use only 3, which is the obvious minimum. However, some have 4, which results in some redundancy.
With 4 wheels, you really can only rely on 3 of the wheels having good contact at any time. I imagine that the 4 wheel version is just to improve stability within the footprint of the vehicle. I.e. for the same amount of stability using 4 wheels, you would have to have a larger footprint if you only used 3.
Any other insights?
Joe Dunfee
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THe math for a 4 wheel design may be easier to digest. If the wheels were on a proper suspension mechanism, then you could take advantage of 4.

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