?: 3-connected Counterexample

$ |VG|=8 $
$ |EG|=12 $
$ VG=\{a,b,c,d,e,f,g,h\} $
Adjacency matrix (in alphabetical order): \[ \left( \begin{array}{llllllll } 0&1&1&0&0&0&0&1 &  1&0&1&1&0&0&0&0 &  1&1&0&0&1&0&0&0 &  0&1&0&0&1&1&0&0 &  0&0&1&1&0&0&1&0 &  0&0&0&1&0&0&1&1 &  0&0&0&0&1&1&0&1 &  1&0&0&0&0&1&1&0 \end{array}\right)\]

For the explanation, see the following comment. -----------

It could be so that I am making a mistake, if so, please explain my mistake to me.
I came to this point by simple trial and error.
I would like to upload a simple picture, but I seem to be a little lost on how to do this.

Nieke Aerts

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