I'd like to be able to generate visualizations of the pentagon Goldberg Polyhedra from scratch (i.e. I'm looking for the math, not a software library or package to do this).
I can generate truncated subdivided icosahedra, and therefore I can generate their duals: the $G_V(0,n)$ Goldberg polyhedra.
I realize that for a general Goldberg polyhedron, the faces are not regular, and so there is no one obvious $G_V(m,n)$ polyhedra to generate. I'm looking for approaches that can generate a representative polyhedra where the faces are near to regular, and where the vertices are near to lying on a sphere.
Because my application is visualization, I'm rather flexible on what `near' means.
I understand that Goldberg polyhedra are duals of particular Geodesic spheres, and I understand how to construct the dual, so if there is a resource I'm missing on generating the geometry of geodesic spheres, I'd be happy with that. (All the resources I can find on geodesic spheres only give constructions of the subdivided icosahedron, which only give the $G_V(0,n)$ polyhedra.)