The applet below shows a stellated dodecahedron. Its 60 triangular faces are colored with 6 colors in a nicely symmetrical way. If you click near one of the vertices you can see the pyramid at that vertex spin, destroying some of the symmetry. If you click with the middle mouse button you spin the star beneath the pyramid (but the pyramid doesn't move).
If you do this a few times you will have scrambled the whole thing. If you've forgotten what you did you've made yourself a puzzle - solve it by returning the figure to its original state.
This figure is really three dimensional. You should be able to rotate it by dragging the mouse (you can in the mathworld page linked above) but I haven't programmed that yet. You can make any vertex the top or the bottom (from your point of view) by choosing the appropriate option from the pull down menu right click shows you.
You can get more help from the Help menu, of course.
Note: if the applet fails to open you may need to change the security settings for this page in your browser.
There's nice mathematics about this puzzle - some known, some waiting to be done. Here are slides from a talk I gave: From Kepler's Echinus to Rubik's Stellated Dodecahedron and a rough outline of a paper waiting to be written.
If you want to run this applet as an application you will need to install Java 5.0 and download gadget.jar from this page. (Your browser may think the jar file is a zip file, and name it "gadget.jar.zip". If so, change the name.) Then double clicking the jar file will start the application.
Warning: the mouse misbehaves! From time to time mouse seems to stop responding - I think more for middle and right mouse buttons than for left. Use the keyboard shortcuts (described in Help) to reduce frustration - they work much more often. If you think you can fix this problem look at the bug report.
This page lay dormant for several years. In the summer of 2010 I finally asked Melinda Green for help. She suggested I join the 4D cubing Yahoo group. Here's a link to what I asked there.