Geodesic shapes are spherical surfaces that consist of triangles. I wrote a POV-Ray macro that allows you to include a wide variety of these shapes into your scenes.
A sample scene of my macro 'geodesic.inc'. All the shapes seen in this image are created on the basis of geodesical spheres, i.e. spherical shapes with a triangular structured surface.
Here you can see the evolution of geodesic shapes from the basic polyhedra tetrahedron, octahedron and icosahedron.