In each case, give the values of r, e, or v (whichever is not given) assuming that the graph is planar. Then either draw a connected, planar graph with the property, if possible, or explain why no such planar graph can exist.
I'm stuck on this one: 17 regions and every vertex has degree 5. Using Euler's formula, I believe it would be v - 34 + 17 = 2 with v = 19 which gives a valid answer because using 3V-6 theorem, 57 - 6 >= 34? But the answer is that it's not possible, why?