I am one of the "stereo-blind" individuals Dave Stanke discusses in his Chapter 9 response. Except under rare circumstances, I only see with one eye at a time, though which eye I am looking with can change suddenly, either automatically or by my own volition. For the most part, my vision is normal - close one eye and you will find that very little looks different. My lack of depth perception is most apparent when there are few or no pictoral cues - I am not very good at catching pop-up flies, and I could not receive a pilot's license. Also, I cannot perceive stereograms or other illusions requiring binocular vision.
I am not sure whether lacking depth perception in any way affects my perception of any models of fourth-dimensional figures, whether positively or negatively, but I am willing to act as a guinea pig if anyone wants to study this phenomenon.
I agree with Kenny that a multimedia Beyond the Third Dimension would have many advantages over the current edition. Since this is not yet an option, we must look beyond the book for examples of animation. I would definitely like to watch the hypercube film again. Also, would it be possible to reserve time in the SunLab so our class could play with fnord?
Stereographic projection is only one method cartographers use to put a round planet on a flat piece of paper. This page is a very thorough discussion, with images, of dozens of different map projections. The Dymaxion projection, created by Buckminster Fuller, makes use of an unfolded icosahedron, and this page contains both images and an animation of the unfolding.