For a number $n\ge 2$, we define a set of points in $A_{2n}=\{(i,0,0)\in\mathbb{R}^3|1\le i\le n\}\cup\{(0,n,j)\in\mathbb{R}^3|1\le j\le n\}$.
What can we say about the number of vertices in the Voronoi diagram of this set? I know that a vertex will have four points from the set that are at the same distance from it, but I don't see if this helps me with finding a lower bound.
(I was told that I should get that it is bigger than $cn^2$ where $c$ is some constant, but I'm don't see why this is, or what the constant will be)
Thanks for any help!