UV mapping for sculpties

For simplicity let's discuss a sphere 4x3, the same principles will apply to a sphere with 32 vertices per slice.

Here is the sphere.



Ok, it doesn't look much like a sphere, but with a stress of imagination ...

Vertices are numbered 0-9 and faces designated with letters a-p (only some of the visibile elements have been marked to avoid confusion).



Here is how the vertices are connected with the association faces -> vertices:



Now, the UV mapping for each face is: