Three-dimensional, highly symmetrical, star figures, or "stellated polyhedra", have fascinated me for many years. I hope to produce and sell inexpensive software that makes it easy to display, and manipulate, these beautiful forms.
The first edition, which runs on Mac OS X, is freeware (I used it to make the image above the first paragraph):
Here is a copy of the first edition thqt will run on older Macs with Ppc processors.
The second edition is taking a long time to complete. One of the challenges is to count the number of stellations of a polyhedron. Here is a paper explaining how this can be done and giving preliminary results.
Vladimir Bulatov makes striking works of art based on polyhedra, and published an applet which draws many stellations. Interestingly, he allows for different symmetry groups, between the special or general group and the trivial group.
Robert Webb sells Small Stella, Great Stella, and Stella 4D; these are programs which run on PC hardware. The first two draw stellations, along with many other things.