Hi Steve,
The only regular equispace spherical patterns are those corresponding to the faces or vertices of the five regular polyhedra: Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron. As such the only possibilities for equispace patterns are those with 4, 6, 8, 12, and 20 instances.
If you examine objects like golf balls you'll see that they aren't exactly equispace.
Thanks,
Mike Foster
ATK