I have always been fascinated by stellations (even before I understood them). For example, the image in the upper-left corner of this page is the third stellation of a regular dodecahedron.
Vladimir Bulatov has written a great Java application for exploring stellations of a wide variety of regular polyhedra. I’ve never gotten the applet to launch properly from the web page, but after downloading it, it worked great. And: the source is available to tempt me to fiddle with it (must resist, must resist..).
Here’s an example of a stellation of the truncated cuboctahedron:
If you don’t know what a stellation is, just poke around anyway. It’s cool.