Question 178
For a given positive integer $n \gt 2$, let $C_1$, $C_2$, $C_3$ be the boundaries of three convex $n$-gons in the plane such that the sets $C_1 \cap C_2$, $C_2 \cap C_3$, $C_3 \cap C_1$ are finite. Find the maximum number of points of the set $C_1 \cap C_2 \cap C_3$.