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.
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.
Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area.