I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it.
Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape?
If I must make myself clear (because I'm pretty sure my terminology is indescript and probably completely wrong), when I say "coplanar faces", I mean faces that can have a ruler lay flat across them. So, not parallel or intersecting. Each face in the shape must have at least one coplanar match.
Thanks a whole bunch in advance.
Edit: Rahul has found a shape that fits the description (the small stellated dodecahedron with the faces interpreted to be triangles, see the comments below). Thanks, Rahul!