Looking at https://en.wikipedia.org/wiki/Goldberg_polyhedron for specifications
- GP(m,n) or GP5(m,n): standard Golberg polyhedron (12 pentagons + the rest hexagons).
- GP3(m,n): 12 triangles + the rest hexagons.
- GP4(m,n): 12 squares + the rest hexagons.
(This would also give us the geodesics, by taking the dual of the Goldbergs. We can also get the geodesics in other ways.)
I might work on a PR for this someday, but wanted to put the idea out there for anyone else interested.