I have a sphere and I have to place some points on it, the most uniformly possible.
If I have 4 points, placing them as vertices of a tetrahedron seems good. If I have 6 points, placing them as vertices of a octahedron seems very good too.
How can I find a way (the best if it exists) to place only 5 points ?
EDIT : "Uniformly" would mean that if I draw a Voronoï diagram on the sphere, each point has a same-area cell and the diameter of a cell is minimized (they are "round" and not some thin slices of the sphere).