Projection of a n-dimensional simplex given its edge lengths

Hi, I posted this question in pre-universitary geometry forum, but I am not sure whether it was the right one, so I am trying in this more advanced forum. I apologize if re-posting it here is not appropiate.

My question was the following:

I have the set of distances between the vertices of a n-dimensional simplex (for instance a tetrahedron in 3 dimensions) and I would like to calculate the distance between each of the vertices and its centroid. For this purpose, I need any possible configuration of the coordinates of its vertices, however I am not able to find the right solution (even an algorithm) for this.

Any guide, hint, or help will be very wellcomed!

Thank you in advance.