Given radius, and many vertices on it, how can I find center of a sphere? I have a sphere, I know its radius. I also have the coordinates of 500 vertices which are on the sphere. How can I find the center coordinates of a sphere? Is there an easy way to do that? Thanks.

You need just four vertices $A,B,C,D$. Let $O_A$ be the circumcenter of $BCD$ and $l_A$ the line through $O_A$ that is orthogonal to the $BCD$-plane. Let $O_D$ be the circumcenter of $ABC$ and $l_D$ the line through $O_A$ that is orthogonal to the $ABC$-plane. Then $l_A$ and $l_D$ meet in the centre of the sphere.
