2. It actually looks more like a redefinition than a new discovery: "It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces "
"Schein and his colleague James Gayed have described that a fourth class of convex polyhedra, which given Goldberg’s influence they want to call Goldberg polyhedra, even at the cost of confusing others. "
Then, recurse!
Inflating two adjacent surfaces creates a valley along the pre-existing edge between the two of them and fails the above definition.
As far as I can tell, the discovery here (if there is one at all) is a method for constructing those polyhedra and others like them and being sure they're actually polyhedral (no curved or bent faces).