I made this faceting of the rhombicosidodecahedron using Stella 4d: Polyhedron Navigator. You can try this program out, for free, at http://www.software3d.com/Stella.php.
A Faceting of the Rhombicosidodecahedron
RobertLovesPi.net
Polyhedra, tessellations, and more.
RobertLovesPi.net 
Robert, does Stella tell you the dihedral angle measurements? I’m looking for software that has that capability… And conversely, to be able to specify dihedral angles? Thanks
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I had never tried to do this before, but it took me less than a minute to figure out how to measure dihedral angles in Stella. As for the converse, I don’t think the software lets you specify dihedral angles, but I could be wrong.
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Why is the rhombicosidodecahedron called that name? None of the faces is a rhombus.
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That’s a good question, but I don’t know the answer.
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I found this Etymology:
From rhomb(ic) + icosidodecahedron, referring to the fact that the 30 square faces lie in the same planes as the 30 (rhombic) faces of the rhombic triacontahedron, which is dual to the icosidodecahedron. https://en.wiktionary.org/wiki/rhombicosidodecahedron
I knew about the duals.
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