I would to know how to uniquely identify a face of a Goldberg (0,n) polyhedron: http://en.wikipedia.org/wiki/Goldberg_polyhedron#Icosahedral_G.280.2Cn.29_polyhedra
It's possible to uniquely assign each face (including the 12 pentagons) to a tuple of values like a Cartesian coordinate system?
If yes, it would really help me to understand this coordinate system, an unfolded version of one of these polyhedra with the coordinates on each hexagon and penthagon.
It would be a very convenient way to automatically check if a face is adjacent to another or how many faces away is.
Thank you for your time
EDIT
I've tried using a 2 axis system, where an (i,j) cell is adjacent to this cells: (i-1,j-1) (i-1,j) (i,j-1) (i,j+1) (i+1,j) (i+1,j+1)
There are many cells with a multiple index (same color = same cell) https://drive.google.com/folderview?id=0ByLsSaTtv19BNjZFTF9wNTNqbVE&usp=sharing
Another attempt is to use the pentagons as a reference for a trilateration system (as showed in the trilateration.png file above). In this case I have a unique index for each cell, but I don't know how to calculate the distance between cells