# generalization of tetrahedron

I just want to know how to locate n+1 points in n dimensional real space such that the distance between any two points is 1 e.g. can you guys help me please?

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I think en.wikipedia.org/wiki/Simplex should be able to help you out. – Ian Coley Mar 20 '13 at 17:01
I think this is not what I want.. – user67458 Mar 20 '13 at 17:08
This describes the general format of the solid whose vertices are exactly the set you describe. The edges are of course wrong. Maybe en.wikipedia.org/wiki/5-cell looks better for your purposes? – Ian Coley Mar 20 '13 at 17:11
It's easier to locate the n+1 points in a hyperplane in n+1 dimensional space. – Johannes Mar 20 '13 at 17:42

## 2 Answers

You might check the proof of

Cartesian coordinates for vertices of a regular 16-simplex?

for a formula for the regular simplex vertices

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In the Wikipedia article under "Cartesian coordinates for regular n-dimensional simplex in R$^n$" a process is described that results in just this. It works in any dimension.

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