Is there a theorem that states that n distinct points in R^n-1 or higher one can be separated in an equal distance as the distance is greater than 0?(adsbygoogle = window.adsbygoogle || []).push({});

We know that 4 distinct points in R^2 cannot be positioned in an equal distance>0 but in R^3 it is possible as a pyramid shape.

If there is such a theorem, could you give me reference?

I've posted this on this area because it seems it is a problem of solving a system of equations.

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# N distinct points in R^n-1 or higher one can be separated in an equal distance(>0)?

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