If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi.

Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirror-image of the polyhedron shown above.

Any chiral polyhedron may be combined with its own mirror-image to create a compound.

This is the dual of the snub dodecahedron’s 43rd stellation.

This dual is also chiral. Here is its reflection.

Finally, here is the compound of both duals.

I used Stella 4d: Polyhedron Navigator to create these images. You may try this program for yourself at http://www.software3d.com/Stella.php.