Had a comment to a post the other day that turned out to be from a high school senior. I checked out her web site where she does incredibly cool geometric stuff... check it out...
This child obviously does not need homework to get an education.
This one is a stellated icosahedron, and apparently there are 59 different versions of it. [You can download a Wolfram Demonstration of them if you have their free player]
This is the kind of stuff Kepler played with when he wasn't measuring the planets. He discovered two of the three stellations of the dodecahedron (there are three in all).
If you are curious, I will tell you that the tetrahedron and cube have no stellations (figure out why they don't), and the octahedron only has the beautiful stella octangula.