Projection of a n-dimensional simplex given its edges

Hello,

That's my first post here, I hope it's in the right thread, if not let me apologize and i will try to fix it!

My question is 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.