Assume that $\Delta \subset \Bbb{R}^3$ is a union $\Delta = \Delta_1 \cup \Delta_2$, where $\Delta_1$ and $\Delta_2$ are pyramids with the vertices $O_1 = (0,0,1)$ and $O_2 = (0,0,−1)$, respectively, over the same convex $n$-gon belonging to the coordinate plane $z = 0$. Find $V$, $E$, and $F$ (the numbers of vertices, edges, and faces) for this polyhedra.
From my understanding, the number of vertices in the figure should be $n+2$, where $n$ is the $n$-gon base of the two pyramids. The edges should then be $3n$, and the faces should be $2n$.
I tried to find the exact value of $n$ by using the $V-E+F=2$ formula but it all cancelled out to give $2=2$. Does this mean $n$ could be any $n$-gon, or is their a specific number for $n$ that I don't seem to get?