This is the 43rd stellation of the snub dodecahedron.
The next one shown is the snub dodecahedron’s 50th stellation.
Finally, here is the snub dodecahedron’s 72nd stellation.
All three of these rotating images were made using Stella 4d: Polyhedron Navigator. You can try this program for yourself, free of charge, at http://www.software3d.com/Stella.php.