IcosiDodecaHedron + 12 Dodecahedrons "molecule"

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12 Dodecahedrons fit very nicely around an icosidodecahedron. They fit so that each dodecahedron shares 5 struts with others. The result ( to a non chemist ), looks like some kind of molecule. In a similar way 20 icosahedrons can be grown around the icosidodecahedron in such a way that they share 3 struts, but I havent built one of those yet.

I made this one out of astro-logix, a fabulous glow in the dark toy for grown ups.

The picture on the right is good of the cats, but not very good as to what is going on in the molecule.

Explanations..

An icosidodecahedrons side's are 6 decagons, which are equators of the sphere. Using radial spokes from the corners of the decagon equators you can build 10 pentagons onto each decagon. Each of these pentagons has 2 shared sides.

 

These pentagons that are built onto the sphere can be completed to form either dodecahedra or icosahedra, by using either the triangles or the pentagons as bases.

In the model on the right I have added one of each, to see how they fit with each other.

 

Two further views..

This one is aligned along the axis of one of the radial struts.
This one is aligned so that you can see through opposite triangles on the icosidodecahedron.

An almost identical construction is described by an old japanese sangaku problem about tangent spheres. see here for a web page