How to plot $N$ points on the surface of a $D$-dimensional sphere roughly equidistant apart? Let's say I have a $D$-dimensional sphere with a radius $R$. I want to plot $N$ number of points evenly distributed (equidistant apart from each other) on the surface of the sphere. It doesn't matter where those points are exactly, just that they are ROUGHLY equidistant from each other. How would I do this?
If $N \le D + 1$ all points must be located on $N-1$ dimension equilateral triangle.

UPDATE

So, I thought today  at this problem and invented method, contains following steps:


Generating $N$ random points on sphere $R$ (that is generating points with coordinates with Gaussian distribution).
Building Convex Hull (or triangulation on hypersphere even better) with generated on first step points. This step can be solved with MIConvexHull library if you familar with C#, similar library on your favorite language or your own code.
Using Genetic algorithm, Simulated annealing or another method of global optimization. This method then have to be applied to variance value of all edge lengths from convex hull from step 2.
If $N \le D + 1$ all points must be located on $N-1$ dimension equilateral triangle.

UPDATE

So, I thought today  at this problem and invented method, contains following steps:


Generating $N$ random points on sphere $R$ (that is generating points with coordinates with Gaussian distribution).
Building Convex Hull (or triangulation on hypersphere even better) with generated on first step points. This step can be solved with MIConvexHull library if you familar with C#, similar library on your favorite language or your own code.
Using Genetic algorithm, Simulated annealing or another method of global optimization. This method then have to be applied to variance value of all edge lengths from convex hull from step 2.