Schoenhardt Polyhedron

This unassuming shape, the [Schoenhardt polyhedron], is actually quite special; it is the simplest non-convex polyhedron that untetrahedralizable (in other words, it cannot be built out of any number of tetrahedra). It has no internal diagonals; every vertex is connected to four others by edges, and the diagonal to the last vertex crosses the valley between two of the sides.

I ran into a discussion of this shape and found it difficult to visualize, even with animated versions like the one on