I am currently reading the paper A Minimal Triangulation of the Hopf Map and its Application. In the paper, the authors are trying to describe a triangulation of the 3-sphere into a (abstract) simplicial complex. It is supposed to have 12 vertices, given by gluing the top parts (before the arrow $\eta$) of Figure 1b and 2b, if I understand it correctly. However, I can't find (or visualize) the vertex $D_2$. I saw $D_2$ appears in the formula $W = D_2 * \partial W$ in Figure 2b, but I'm not sure what does the symbol $*$ really means. Is it some sort of product? I would suppose that this"product" gives an edge from $D_1$ to $D_2$. Also, since $\eta$ is the usual Hopf fibration, I should expect the fiber of each vertex $A,B,C,D$ of the tetrahedron in Figure 2b to be $S^1$, so the vertex $D_2$ must connect to the vertex $D_0$ with an edge, but I can't see how (as $D_0$ only appears on the 3-ball $V$). I think this has something to do with the thing St.$_{\partial V}$ appearing in Figure 2b, but (again) I am not sure what that means.
Thanks for the help.