We define the regular immersed projective solution space for a triangulated 3-manifold, and completely determine it for the figure-8 knot complement. We show that there is a close relationship between vertices of this polytope and normal surfaces of a particularly simple form immersed in the manifold.
"The regular projective solution space of the figure-eight knot complement." Experiment. Math. 9 (2) 221 - 234, 2000.