The compound of five tetrahedra is a geometric object that interests me for a long time. As a freshman, I carefully drew it using compass and straightedge on my notebook. I've always been intrigued by its relation to the dodecahedron, the chirality, and its pretty shape. In short, it's my geometric crush.
So far I haven't seen a twisty puzzle based on this shape. Recently, I decided to write a simulator. That's definitely a good motivation for me to learn Java applet programming. It's done and can be found here:
You may need to upgrade JRE to see it. I call it "Twisty Star" because it's a twisty puzzle, and also the shape looks twisted. Some screenshots:
It's a compound of five tetrahedra intersecting with each other. The 20 vertices coincide with the vertices of a dodecahedron. The five tetrahedra are colored by five colors.
It can be twisted around 20 vertices. Since the cuts are right above the faces of the tetrahedra, it can be regarded as "face-turning" as well as "vertex-turning". In other words, the dual of this solid is its mirror. So it's almost self-dual. Therefore there's a one to one correspondence between the vertices and the faces. Mathematically it's related to the face-turning icosahedra.
The vertex to twist is labeled by a small circle around it, and the moving region is highlighted. Even with these assistances, it's not easy to see how it turns. Sometimes with only one twist away from the solved state, I just can't find the twist. I haven't solved it yet. For this color scheme, I guess it has multiple solved states, meaning that one can, for example, swap the red tetrahedron with the blue one.
I think it's possible to build a physical version. I posted this simulator on the Twistypuzzles forum [http://twistypuzzles.com/forum/viewt...?f=1&p=281801] and request the builders over there to consider it. Maybe someone will make it someday.
I'd like to thank Melinda, Roice, Jeremy and Brandon for their feedback.
Please let me know if you see more glitches. A known bug is that I'm not handling occlusion very well. Some line segments that should be hidden are visible. I may look at some advanced algorithms to fix it in the future.
Have fun solving it!