Before destroying the legs of the Pseudogeodesic sphere to scale 3, it was not very hard to build on them a rhombicosidodecahedron also to scale 3:

However, these legs look too big. Because of that, and of the easy construction of the rhombicosidodecahedron to scale 3, I tried to build one to scale 4. Only, the design of the upper section of the legs had to be adjusted to the new scale (each one requires now nearly 700 rods). But the construction, quite simple at the beginning, collapsed near completion. In my second attempt, really near indeed:

Probably, the construction could be completed using some auxiliary structures. But I think that I will not retry it very soon. This is one of the rare moments in which one regrets having many Geomag pieces.