What dodecahedral molecule is Linus Pauling likely holding in this photograph? Does it have 40 carbon atoms?

Question

The video Quasicrystals ; Prof. Daniel Shechtman ; Nobel Prize in Chemistry focuses on Professor Dan Shechtman but happens to include some photos of Linus Pauling who never believed in quasicrystals. From the video:

The leader of that group was Professor Linus Pauling, a two-time Nobel laureate. He was a very important figure and an idol of the American Chemical Society, and to his last day, he was standing on stages and published papers saying that "Daniel Shechtman is talking nonsense."

During this part of the video there is shown a photo of Linus Pauling holding some ball and stick molecular models. These appear to be dodecahedral arrangements (12 pentagons, 20 vertices) of possibly carbon atoms.

This photo is apropos because early quasicrystal indeed had dodecahedral structure.

But my question is about the molecule for which this is likely the model. I think I see a dodecahedron with one more ball attached to each of the 20 corners. All 40 balls are black, and I'm guessing that if the 20 atoms projected outwards were hydrogen and thus $\ce{C20H20}$ or dodecahedrane) then they would be white in this color photograph. Since all 40 atoms look the same and it's common to leave the hydrogens off when they are understood, I'm wondering if this was supposed to be $\ce{C40H60}$.

I have not found a name for such a molecule with a 20 atom dodecahedral core and 20 more attached to the vertices, the closest I've found here is Tetracontahydrobenzo[5,10]anthra[9,1,2-cde]dibenzo[kl,rst]pentaphene but of course it's flat and made of hexagons rather than pentagons.

Question: What dodecahedral molecule is Linus Pauling (likely to be) holding in this photograph? Does it have 40 carbon atoms?