Thanks to all who contributed to this discussion.  Paul Bourke's site was
interesting.  Ultimately, implementation of the "electrostatic repulsion"
suggestion did the trick.

I generated a desired number of points on the sphere in a random fashion and
then minimized the repulsion between the points.
While testing, a polyhedron with 8 vertices was inevitably a square prizm
rather than a cube...

Ilia



"Christopher James Huff" <cja### [at] earthlinknet> wrote in message
news:cjameshuff-F3FCDE.14012902052004@news.povray.org...
> In article <409495bc@news.povray.org>,
>  "Ilia Guzei" <igu### [at] fozziechemwiscedu> wrote:
>
> > Mersenne twister can probably produce a random enough (as in "uniform")
> > distribution but I'd rather do it exactly if possible.  I need to do it
once
> > to generate an input table for an application, so time and algorithm
> > efficiency is irrelevant.
>
> It is not possible to do so for large numbers of points. As I recall,
> the largest number of points that can be perfectly evenly distributed is
> 20, the triangles of an icosahedron or vertices of a dodecahedron.
>
> If you need points with overall even spacing, and the spacing given by
> polyhedron subdivision is too uneven, the electrostatic repulsion method
> mentioned can help you minimize the unevenness. You basically model each
> point as a particle that repels the other particles by the 1/r^2 law.
> Figure out which direction the surrounding particles are pushing each
> particle, move it slightly in that direction and project it's new
> position onto the sphere, and repeat until the particles settle down
> enough.
>
> --
> Christopher James Huff <cja### [at] earthlinknet>
> http://home.earthlink.net/~cjameshuff/
> POV-Ray TAG: <chr### [at] tagpovrayorg>
> http://tag.povray.org/

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