Here is another example with 8 vertices: a short fat Star Trek symbol and a square in orthogonal planes.
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.
Addendum: As Saúl Rodríguez Martín mentions, this example may nor work. If we assume, however, that the links are physical, that is they have some thickness, then I think that the links cannot be separated.