Geometric median of tetrahedron

This activity belongs to the GeoGebra book Attractive projects. 3D project: create automatic dynamic demonstrations. We can generalize the Fermat point, which minimizes the sum of distances to the three vertices of a triangle (geometric median), to space. Now the robot will look for the point that minimizes the sum of distances to the four vertices of a tetrahedron. (Remember that you can rotate the 3D View with the right mouse button.)