Question: How to show that this graph is planar?

I am unable to write a formal proof

[![enter image description here](https://i.stack.imgur.com/xHzg7.png)](https://i.stack.imgur.com/xHzg7.png)

In the book the answer is given that this graph is planar.
Can you kindly say how to prove that this graph has no subgraph homeomorphic to $K\_5$ or $K\_{3,3}$?

I find that this graph has two vertices $[0],[4]$ of degree $8$ and all other vertices are connected to these two. 

How to show that this graph is planar?

Please help.

Answer: 
Just redraw it by pulling out vertex $0$ and bending its edges..
Here is some specific drawing, that proves that graph could be embedded into the plane.

[![enter image description here](https://i.stack.imgur.com/RpDIc.png)](https://i.stack.imgur.com/RpDIc.png)