Yes indeed - we must say what we decide we mean by "evenly spaced"

For the cases N=2,3,4,6,8,12,20,30 it is plain enough

We mean maximally spaced but in groiups as large as possible the distances to be equal

For example for N=8 we want every dot to be equal distance from every other of 3 other dots and equal spaced but more distant from three other dots.

For N=4,5,7,,9,10,11 etc we can make up similar rules

But for all N>4 we need to say what weight we give to the dots closest compared to those farther away. In that way we decide which dot-arrangement is best for each N in turn.

This is where I am stuck and need your ideas and suggestions