If I have a planar Graph $G(V,E)$, it is easy to obtain the dual $G^{*}$ graphically.
But how is it possible to show formal that $G$ has at least two different dual graphs?
Is it enough to find an isomorphic graph to $G^{*}$?
For example the graph with $V$ = {1, 2, 3, 4, 5, 6} and $E$ = {(1, 2), (1, 3), (2, 3), (4, 5), (4, 6), (5, 6), (2, 4), (3, 5)}
How to show formally that this graph has at least two different dual graphs?