There are two Java-based interactive versions of the hypercube available here. Each of them requires you to have a Java-capable browser, and to have Java enabled. See the documentation for your browser to see how to enable Java.[an error occurred while processing this directive]
Interactive applets and instructions for them are available for:
This applet shows the hypercube rotating through the fourth dimension. The rotation is continuous, and you can change the plane in which the rotation occurs.
This demonstration uses a parametric-graphics applet developed at Brown University. The applet lets you move through four-space by adjusting angles of rotation in two different planes. This hypercube is actually a coarse parameterization of a torus on the three-sphere in four-space; you can increasse the number of facets used and thereby make the torus smoother.