The last one I gave involved a cube. This one uses a tetrahedron.

Imagine the tetrahedron with one triangular face at the bottom. We are going to connect the midpoints of two of the edges. Choose as one edge, one of the edges not in the bottom triangle. Choose as the other edge the only one that does not intersect the first one, which is located in the bottom triangle. The rotation axis is the line through the midpoints of the two edges.

Can you see that a 180 degree rotation leaves the tetrahedron occupying the same space? I can’t see it yet. I can see that the two edges attached to the rotation axis end up on top of themselves in the opposite direction. Where does the bottom face go? I wish there was an animation for this. I will have to see if I can construct a tetrahedron.