The Boundary of a Hypercube

The boundary of a solid hypercube?

 $\partial(I\times I\times I\times I)$ $=$ $\partial((I\times I)\times(I\times I))$ $=$ $\partial(\square\times\square)$ $=$ $(\partial\,\square\times \square)\cup (\square\times \partial\,\square)$ $=$ $(\box\times\square)\cup(\square\times\box)$