Prove that this graph is nonplanar Can anyone show me why this graph is nonplanar (which Mathematica assures me to be the case) ?

The graph passes the simple test $e \leq 3v - 6$.
I have tried and failed to find subgraphs isomorphic to subdivisions of $K_{3,3}$ or $K_5$.
The subgraph arising from deleting the right-most vertex and its adjacent edges is also nonplanar. In that subgraph, since only 3 vertices have degree 4, I suppose we cannot find a subdivision of $K_5$, so there must be a subdivision of $K_{3,3}$, but I cannot see it.

You can find $K_5$ in your graph, here it is:

I hope this helps $\ddot\smile$
