If we are asked to place 3 points on the surface of a sphere so that they are equidistant, it's easy to visualize that the result will be such that the three points form an equilateral triangle. If asked to place 4 points it's easy to visualize that the result is such that the points arrange themselves into a tetrahedron. It is impossible for me to visualize what happens with 5 points, there is apparently no solution. So what would happen if we imagine an actual physical system where each of the five points has some kind of 'motor' which constantly repels it away from whichever other point it is closest to. Would the 5 points ever settle into some kind of recognisable arrangement? What we expect to see as the motorised points attempt to reach an equidistant configuration? What sort of math applies to resolving this question?