Stressful

Six binder clips prop each other open.

Designed and constructed in April, 2011.

The handles of six binder clips weave together in a way that holds all clips open. This "explosive" configuration is quite stable despite its high potential energy. I will leave the construction method as an entertaining puzzle. Here's a hint: you should need to strain your hands no more than when normally opening a binder clip.

The 24 symmetries are the same as those of a volleyball, namely, the Pyritohedral group.

Update: by request, here are a few more assembly tips:

Hint 0: The silver clip bodies can (and must!) be removed from the black clip bodies.
Hint 1: Prop each of the clips open with, say, another clip. This removes much of the "stress" from the assembly process and avoids finger damage/pain.
Hint 2: Build the entire thing first with "backwards" clip bodies, i.e., with the bodies closed and facing outward instead of open and facing inward. Afterward, use the previous hint to replace the bodies in the correct orientation. This postpones all tension concerns until the very end, after the handles have been fully woven.
Hint 3: Each of the 12 handles weaves around precisely 4 other handles. As in the previous hint, attach handles to "backwards" clip bodies as you weave them so the handles don't fall out.