The second stellation of the dysdyakis triacontahedron, seen above, is an interesting two-part polyhedral compound. The dysdyakis triacontahedron is one of the Catalan solids, and is the dual of the great rhombicosidodecahedron.

There’s also a “little brother” to this first compound — it’s the second stellation of the dysdyakis dodecahedron, which is the dual of the great rhombicuboctahedron. Like its “big brother,” it’s a two-part compound, and is shown below.

Interestingly, the components of these two compounds are “stretched” versions of two other Catalan solids: the pentagonal hexecontahedron (dual of the snub dodecahedron), and the pentagonal icositetrahedron (dual of the snub cube).

I made these virtual models using Stella 4d, which you can download and try for free at http://www.software3d.com/Stella.php.