Do determine a circle, you would need at least three coordinates. How many are necessary to determine a sphere?
I believe the answer is 4 (and hopefully someone will correct me if I'm wrong...). Here's why. Any 3 points are coplanar. Consider 3 points on the plane A, B, and C. One can connect each pair of points with a line segment to create a triangle, then circumscribe a circle. The center of said circle is equidistant to all 3 points. Consider a line perpendicular to this plane. It is easy to prove that any point on this line is also equidistant from A, B, and C. Therefore, it must take more than 3 points to determine a sphere.