Let's consider 3 spheres in plane xy and 1 sphere above them, the fourth sphere have equal distance from 3 spheres, if we project these distances on plane xy, these projected lines have still equal size, so, the fourth sphere is above of center of triangle. The center of triangle is also in h/3 of edge.
Let's consider 3 spheres in plane xy and 1 sphere above them, the fourth sphere have equal distance from 3 spheres, if we project these distances on plane xy, these projected lines have still equal size, so, the fourth sphere is above of center of triangle. The center of triangle is also in h/3 of edge.