The polyhedral compound above is actually a compound of two compounds: the compound of three cubes (red, yellow, and blue), as well as the cube/octahedron base/dual compound (green and purple). The dual of this five-part compound is shown below, still with the cube/octahedron compound in green and purple (it is its own dual), and with the three parts of the compound of three octahedra in red, yellow, and blue.

I created these using the “add/blend from memory” function of Stella 4d: Polyhedron Navigator, one of this program’s capabilities which I have only recently begun to explore. You may try this software for yourself, for free, right here.