Here is another example with 8 vertices: a short fat Star Trek symbol and a square in orthogonal planes.

[![enter image description here][1]][1]
Since the distance between the base points of the red figure is greater than its height, one cannot rotate the square to take it out.


  [1]: https://i.sstatic.net/TiQQK.jpg

**Addendum:** As Saúl Rodríguez Martín mentions, this example may not work. If we assume, however, that the links are physical, that is they have some thickness, then I think that it should work.