Slice that Polytope!

A 4-dimensional convex polyhedron (properly called a “polytope” or “polychoron”) is a volume of 4-dimensional space that is bounded by a number of hyperplanes. (…) These 4-dimensional star polytopes cannot be viewed directly in 3 dimensions. What we have to do is slice the 4-dimensional object with a 3-dimensional hyperplane. The part that intersects the slicing hyperplane forms a 3-dimensional star polyhedron, which is displayed by the applet in stereoscopic 3D.

I recognize that these explanations can be intimidating if you are not familiarized with polyhedra. That´s why the site above is invaluable: it will let you intuitively tinker with those abstruse geometries through a java applet with an easy to use interface. There´s a huge amount of 3D shapes to explore (you can click on the shape and drag the mouse to rotate it), and with several different rendering options, a Stereo Mode for 3D visualization and automatic rotation and animation features, this little applet could keep you entertained for ages (plus it is highly inspirational for designers and modular origami enthusiasts). A must see!

ps. You can also visit this page and download another very easy to use program that allows you to manipulate and transform different polyhedra. For general information on polyhedra, this page looks like the place to go.