thank you very much for your reply
this method in principle works well, but for example, in the cases below it gives a result with reference to a group of points, but in fact the point farthest from this group of points lies on the other end of the sphere?

Mahdiyar, thank you very much for your reply
Now your definition is looking for the most remote in the group of given points
I probably didn’t exactly put it
you need to find the most distant point from this group of points, those should have a little shovel on a new sphere that is maximally remote from each of these points

Below is an approximate point and definition, but it does not quite work correctly

seghierkhaled, yes, the distance between the points must be determined by the sphere, not by a straight line there is a group of points lying on the sphere, you need to find (generate) the most distant point from this group of points on the sphere

I will try to explain
the red dot should be as far as possible from all other points on the sphere
it must be calculated / built geometrically it is not there initially
initially there is a sphere and a group of points lies on it, you need to build such a point that would be removed as far as possible from the existing group of points on the sphere, the distance must be measured over the sphere

Pt_Nemo.gh (14.7 KB)
Here’s my attempt.
I believe pt nemo is coincident with one of the edges sharing 3 cells on the 3d voronoi… can’t counter-test so i’m not sure.