Sorry if I used wrong words - English is not my native language, and I never actually studied geometry.
For a project I'm working on, I need to calculate set of points, that:
- are in given, constant, distance from given source point
- are equally spaced from each other
- surround the source point from all sides
In 2d, I could have done it, but in 3d I'm at loss.
For 4 points, the points would looks like "pyramid" with source point inside, in the middle. For 6 points, I could have got 4 points in one plane, 90 degrees from each other, and 2 points on "poles". But how to calculate it for (more or less) any number of points?
They won't be truly equidistant from the neighbors unless they are on a Platonic solid. That only works for $4,6,8,12,$ or $20$ points. The best alternate packings are often quite complicated. This site has a large bibliography. It has been considered on stack overflow You can search for "packing points on a sphere" and find many hits.