"Mike Williams" <nos### [at] econymdemoncouk> wrote in message
news:42494252@news.povray.org...
> Inspired by the "math related image" thread.
>
> Sphere-6-5: Most vertices have 6 edges, but the red ones have 5. I think
> this is a standard Geodesic Dome.
>
> Sphere-6-4: Most vertices have 6 edges, but the red ones have 4.
>
> Sphere-4-3: Most vertices have 4 edges, but the red ones have 3.
>
> Sphere-6-3: Most vertices have 6 edges, but the red ones have 3.

Nice pictures! I like (from an aesthetic point of view) the cube
subdivision one the best.

Recursive subdivision of the regular tetrahedron (each triangle into
4 new triangles all with vertices on the circumscribing sphere) results
(at stage 3 IIRC) in a non-convex polyhedron with triangular faces.
This surprised me when I first realized it 10 years or so ago.

No such problems with the octahedron or icosahedron.

Jim Buddenhagen

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