We have been given $n+1$ points $v_0$,$v_1$,$\dots$,$v_n$ in general position in $n$ dimensions where $n\geq2$
what is the formula for the center of the simplex?
If say some $k+1$ of the points (where $k$ is in $\{2,2,3,\dots,n\}$) lie on the same $k$-dimensional hyperplane, would the center formula for the lower dimensional simplex be any different?