A view of this surface is given below.
Additional pictures are available.
The dotted line represents the self-intersection. To see that it is an immersion, we need to check that the star of each vertex is embedded . This can be seen in the triangulation above, since the double locus does not contain any vertex. As expected, its image is the wedge of three circles , their common point forming the required triple point in the immersion . To check that it is tight, one must show that all the edges of the convex hull are contained in the surface itself, and that any vertex that is not a vertex of the convex hull of the surface lies inside the convex hull of its neighbors .