Could you find a 3-Regular Connected Planar Graph on $10$ vertices with $8$ faces? If so, explain carefully.
I don't know what does regular mean. I think that 3-connected graph on 10 vertices with 8 faces. From eulerian formula : $v + f - e = 2:$ $10+8-e=2 \Longrightarrow e=16$. And I use other proof "A simple planar graph on v 3 vertices has at most $\;3v- 6$ edges." $\Longrightarrow 30-6=24$ edges at most. I said that $24>16$, if so it can be.
Is it true or not?
Thank you for your answers in advance.