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?
You might check the proof of
for a formula for the regular simplex vertices
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.