After stellating the snub cube many times (so many that I lost count), I ran into this two-part compound of irregular dodecahedra.

Like the snub cube this is derived from, this compound is chiral. Because of this, a four-part compound can be formed by combining this polyhedral compound with its mirror image.

I did all of this using a program called Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.