Euler's formula + Handshake Theorem

Using Euler's formula and the Handshake Theorem, how can I show that this graph is non-planar?

The number of vertices is 8
The number of edges is 14
The number of faces is f
Then, 8-14+f=2 if planar.
Thus,
f=8
Which is not true.

I did it this way because I was too lazy counting all the faces.

I actually counted 21 edges, am I wrong?

Euler's formula states that v+f = e+2

Here

v=8
e=21
f=?

so 8+f=21+2
f=15 which is not true as there are many more. Hence the graph is non-planar.

Using the Handshake Theorem that states that 2e >= 3f
we get ( 2(21) )/ 3 >= f which gives f <= 14 which again is not true, hence the graph is non-planar.

Am I correct?