Distance patterning on a spherical face

[Carbonated]

Hi all,

I'm trying to pattern a body on a spherical face with only a constant distance between the bodies as a guideline. The patterning methods I am familiar with do not allow for this result with a spherical body as base. Do you have a recommended way to achieve this?
Attached pictures of the geometry to replicate.

Thanks in advance,

 

[cowski]

Creating an arbitrary number of equidistant points on a spherical surface is a problem with no solution. There are some good approximations, but no closed form solution.