buckySphere.ma (scroll to the bottom to download related material)

After some experimentation I realized that my last tutorial on this topic creates a sphere that is not as uniform as one might wish. Here is a better solution to the problem of creating a sphere with a uniform triangle distribution.

1. MENU "Create: Polygon Primitives: Platonic Solids"
In the options set the platonic type to "Icosahedron".

2. MENU "Mesh: Smooth"
3. Edit the resulting polySmoothface node:
method = "Linear"
subdidivisionLevels =1
divisionsPerFace = 10
pushStrength = 1.0
roundness = 1.45 (1.5 did not seems to be quite as accurate a sphere shape, although I dont' know the correct mathematical value)

buckySphere.ma (scroll to the bottom to download related material)

This method still has some artifacts and the sphere is not quite perfectly round. For more triangles one could go to a subidivisions of 2, although the roundness and/or pushStrength may need to be adjusted. I found that using higher subdivision levels with lower divisions per face one needed a higher roundness(10) and a lower pushStrength(.15). The higher subdivisions seem to provide a slightly more uniform triangle size, but the shape is less spherical. Alternately one could also apply a second smooth, which may provide the best result. There are simple recursive methods of computing a near perfect sphere, but non of these are implemented in Maya currently. However there is the a mel script called geoSphere on highend3d.com, which looks like it should work well, although I've not tried it.