[size=85]By optimal placement we mean the placement of points on the sphere in such a way that each point is the geometric median of all its other points. The algorithm allows you to find [b]only[/b] the placement with the values of [b]highest Distance Sum[/b]. To find other symmetric arrangements of particles on a sphere it is possible (for example) as in [url=https://www.geogebra.org/m/hw9hhq3h]https://www.geogebra.org/m/hw9hhq3h[/url]. As it turns out, [br]-for optimal placements, it is characteristic that the each point is not only a geometric median but also the geometric center of all its other points,[br]-for a given number of n points, the number of different such optimal placements on the sphere can be 0, 1, 2 , ... . [br] An example is the case of n=8: 1, 2, 3. The second solution corresponds to the case of uniform distribution of points on the sphere. For the cases n=12 and n=14 are found two optimal placements.[br] Examples n=60, 120 are close to a uniform distribution of points on the sphere and are not optimal![/size]