Triakis truncated tetrahedra have the property of packing neatly in 3D space, if you have enough of them:
There are a few other shapes that fill space. Here are a few symmetric ones. There are many other less symmetric ones.
Send ttt_mm.stl to your favourite printing service and they will post you these:
If you want to make your tetrahedra out of card you can print this template:
Photo:
I got as far as making one before getting bored. Let me know if you manage to make more!