A Square Cross a Solid Square

 What is $\box\times\square\,$? Each edge of $\box$ is an interval. An edge crossed with $\square\,$ forms a cube. So $\box\times\square$ is four cubes attached end-to-end. I.e., a polygonal torus. There are two of these, making up all 8 cubes of the surface of the hypercube.