To preface: I'm not looking for the answer to this question. I just need help understanding what the question is asking. I know a fair bit about planar graphs, but not a ton.
"Every vertex of a finite planar graph is the intersection two squares, one triangle, and one hexagon. Either show why this can’t happen, or find how many vertices, edges, and each type of face are in the graph."
So in this question, what exactly does it mean by "the intersection of two squares, one triangle, and one hexagon."
I'm envisioning a planar graph that is 10 vertices, 13 edges, and 5 faces (which obeys Euler's formula). I started by drawing a hexagon, then on 2 of its outside edges, I drew squares that share one edge with the hexagon. Then I drew a single edge from the corner of one square to the other to make a triangle. Am I even close?