N=2 Particles

2 particles repelling each other while constrained to lie on the sphere will "try to get as far as possible from each other". This results in two antipodal points {x,y,z} and {-x,-y,-z}. One standard choice is the north pole {0,0,1} and the south pole {0,0,-1}.

Potential = .5

The convex hull of two points is not a three dimensional figure, so we give no picture, nor projections.

The points:

{{0,0,1}, {0,0,-1}}