"hermans" <sas### [at] telenet_invalidbe> wrote in message
news:4242fec1$1@news.povray.org...

[...snip...]

> Why don't you take the 20 points on the sphere as the vertices of a
> regular icosahedron?

Because the regular icosahedron has only 12 vertices.  It has 20 faces,
so one might try the centers of those faces for the 20 points, but that
fails also because the convex hull is then the reg dodecahedron which
does not have triangular faces.

> In that case all the triangles aren't "as close to
> equilateral as possible" but equilateral. The dual polyhedron is a
> regular dodecahedron (as can be seen on my site and on many other
> sites). For similar arrangments of more points in many cases one can use
> the theory of geodesic spheres (domes). Also in povray a lot of examples
> exist.
> Herman Serras
> http://cage.ugent.be/~hs

Jim Buddenhagen

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