The first image shows a central yellow rhombic triacontahedron, with smaller, blue rhombic triacontahedra attached to each of its thirty-two vertices. The second polyhedron shown is the dual of the first one, with colors chosen by the number of sides per face in the second image — pentagons red, and triangles yellow. The convex hull of this second polyhedral complex shown would be an icosidodecahedron, itself the dual of the rhombic triacontahedron.
I use software called Stella 4d: Polyhedron Navigator to make the rotating polyhedral images on this blog. You can try Stella for yourself, for free, at http://www.software3d.com/Stella.php.
RobertLovesPi.net 
What will be the result if you make the rhombic dodecahedra attached to the rhombic triacontahedron by the edges? What will the dual be?
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I don’t know. Have you tried doing that with the free trial Stella download at http://www.software3d.com/Stella.php?
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Have you tried stellating it?
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I have not, nor did I save a .stel file which would make doing so easier than starting from nothing.
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