A Cube 2-Compound is a union of two cubes. Technically, what I've built is not a Cube 2-Compound, because I have just built the edges of the two cubes, but not the edges that result from intersecting the faces of the cubes, because I couldn't figure out a way to do it. Nonetheless, I think it's a nice construction

The two cubes are double-sized short. Their edges are yellow. First, I constructed one cube. I supported each face with four blue long bars and, because that isn't enough to make the cube stable, I supported it from the inside with red bars. I could not put more support on the faces because that would have made it impossible to add support for the second cube afterwards. Adding the second cube was comparatively easy. Some of its edges have to be supported by long bars (also blue).

A cube-octahedron compound is the union of a cube and an octahedron.

The edges of the cube are yellow and those of the octahedron are blue. The red edges are those that result from the union, i.e., they are intersections of the faces of the cube and the octahedron.

This is some large concave polyhedron which I came up with by accident during the construction of something else (which ultimately failed because it was too heavy). I have no idea if there is already a name for this abomination, but if there isn't, I don't want to come up with one.