Here's the first-draft version of my applets that show you what happens when you truncate, expand, and snubify the Platonic solids. The interactive applets really help you see what's going on -- for instance, the icosahedron is a snub tetrahedron, but it's very hard to visualize that.
Each applet has a line segment with a black dot which you can slide back and forth to see what happens.
These applets are not very polished, but the underlying math is correct and they basically work. I'm working to improve these and eventually submit it to JOMA. I'm not sure if I want to implement the applets using LiveGraphics3D or JavaView (what is it with Germans doing computer graphics with Java?); LiveGraphics is pretty lightweight, easy to work with, and my colleague Jon Rogness has done amazing with it -- but its clipping algorithms work rather poorly. JavaView is vastly more powerful, but has this irritating registration requirement, leaks memory like a sieve, and the .jar files are much bigger.
--Dan Drake ()In some web browsers, the mathlets will become active once you move the mouse pointer over the picture; in others, you might need to click on the picture first. Once active, you can use the following controls: