> > > 3(traingle), 4(tetrahedron), 6(octahedron), 8(cube) and some more. I
> The "optimal" solution for n=8 is not the cube, but a pair of
> parallel squares rotated by 45 degrees (which is probably what
> Anders means).

.. and what I mean :)  : If a cube is enclosed by a sphere, it touches
the sphere's surface at 8 points.

> The first thing Peter would have to decide is whether
> he wants something which looks regular (e.g. platonic solids), or
> something which has optimally distributed points (with respect to some
> repulsive force).

I would like to be able to create both. I find the exact solution
mathematically challenging and the numerical approximation interesting
as it allows to render nice animations of rearranging points.
It all started with the plan to build a lamp with 15 small bulbs (bad
number) on a hemisphere. Since then I thought of several things to
render with such an algorithm, e.g. spikes on sphere-shaped creatures.

> The general solution to the former is probably to start with
> one of the 5 platonic solids and regularly subdivide the faces
> (this gives geodesic domes).

Does subdivision work with the cube and the dodecahedron?

Ok, with subdivision of triangles like this

      /\
     /  \
    /    \
   /______\
  / \    / \
 /   \  /   \
/_____\/_____\

..we can realize objects with the following number of verteces:

From tetrahedron :  4, 10,  34, 130,  512, ...
From octahedron  :  6, 18,  66, 258, 1026, ...
From cube        :  8, ?
From icosahedron : 12, 42, 162, 642, 2562, ... (is this correct?)
From dodecahedron: 20, ?

Bucky-ball (C60-Fulleren): 60, ?

Is there an exact solution for 5, 7 or 16 points?

/PETER/

-- 
Peter Santo (PUMP development)
Visit: http://www.ieee.rwth-aachen.de/mp3/

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