The dual of the snub dodecahedron (above) is called the pentagonal hexacontahedron (below, left). The compound of the two is shown below, at right. (Any of the smaller images here may be enlarged with a click.)
Like all chiral polyhedra, both these polyhedra can form compounds with their own mirror-images, as seen below.
Finally, all four polyhedra — two snub dodecahedra, and two pentagonal hexacontahedra — can be combined into a single compound.
This polyhedral manipulation and .gif-making was performed using Stella 4d, a program you can find here.