The central small stellated dodecahedron is augmented on two opposite star-faces by additional small stellated dodecahedra.
I made this using Stella 4d: Polyhedron Navigator, available at http://www.software3d.com/Stella.php.
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RobertLovesPi.net 
Thank You! Robert, I love your energy and work Thank You are you doing any work in Curved Polyhedra, Non-Euclidean Geometry, and other logic structures. Do you see any value in collaboration to promote and preserve this very rare and unpopular field I believe is the most powerful hidden knowledge of our space, time and energy!
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I tend to stay Euclidean, but I know many people who enjoy exploring non-Euclidean spaces. As for the collaboration you describe, we agree completely.
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