The cube and the octahedron are dual to each other, and can be combined to make this well-known compound (below; can be enlarged with a click).
In hyperspace, the analog to the cube is the tesseract, also known the 8-cell, the octachoron, and the hypercube. Its dual is the 16-cell, or hexadecachoron, made of 16 tetrahedral cells. The image at the top is the compound of these two polychora, rotating in hyperspace.
These images were made using Stella 4d, available at http://www.software3d.com/Stella.php.