Two Compounds of Skewed Polyhedra, Each with Twelve Total Faces in the Compound

compound with 12 faces total

I found both of these with what one could call “random-walk playing” with polyhedral-manipulation software, Stella 4d, available here, with a free trial-download available. In the figure above, both compound components are skewed cubes, while the image below shows a compound of three skewed tetrahedra. Since (2)(6) = (3)(4) = 12, each of these compounds has the same total number of faces, although, of course, the number of faces per component polyhedron varies from one compound to the other.

compound of three skew tetrahedra