This model resulted from Joe Clinton sending me some chord factors for a 3-f geodesic inner sphere inside a Goldberg polyhedron: (i.e. all one edge length).  There isn't a widely agreed way of specifying the different Goldberg polyhedra. Maybe they could be designated as "Goldberg Variation 1, 2,3,4..." etc.  in which case, starting from the upper left corner of the diagram on p.6 of Clinton's Equal Angle Conjecture:
http://www.freewebtown.com/randome/ClintonEqualEdge.pdf
the outer shell of this model would be a "Goldberg Variation 5".

To the far right is a four frequency Goldberg inside and six frequency outside - "Goldberg Variation 4-6". (The outside sphere is entirely hexagons and pentagons whose struts are equal lengths.)

Click on photos to enlarge

 Here's a view of the inside of the above sphere