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How to arrange four points at equidistance?
You have to think 3D!!! A triangular based pyramid does the trick if all the edges are of equal length. .
More generally, you can arrange n+1 points equidistantly (Euclidean… distance) in an n dimensional space, but it is simple to do it in an n+1 dimensional space. First an alogrithm for the n+1 dimensional space followed by an algorithm for an n dimensional space:.
For both algorithms:.
Define e_i as a unit vector in the direction of the ith axis for 1 (MORE)