Two Views of the Compound of the Great Dodecahedron and the Platonic Dodecahedron

I made this using Stella 4d, which you can try for free right here. In the image above, the two components of this compound are given separate colors. In the second picture, below, the coloring is per face, except for parallel faces, which have the same color.

Two Polyhedral Compounds Derived From Catalan Solids

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. It 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

Three Different Compounds of the Octahedron and the First Stellation of the Rhombic Dodecahedron

These compounds differ in the relative sizes of their components. I made all three using Stella 4d, which you can try for free right here.

Two Six-Part Polyhedral Compounds

I stumbled across this compound the other day, while playing around with Stella 4d: Polyhedron Navigator (available here).

At first, I thought this was a compound of six tetrahedra, but careful examination reveals that the tetrahedra are missing parts along the middle of some of their edges. I looked up the canonical compound of six tetrahedra in Stella‘s library, and here it is. As you can see, it’s quite similar — but it does have those “missing” pieces added.

A Compound of the Platonic Octahedron and a Pyritohedral Dodecahedron

The red component of this compound is one of an infinite number of possible pyritohedral dodecahedra. It’s shown by itself in the image below.

I made this compound using Stella 4d, a program you can try for free at