Geometric dual graph

Geometric dual graph --- геометрически двойственный граф.

Plane representations [math]\displaystyle{ \Gamma }[/math] and [math]\displaystyle{ \Gamma^{\ast} }[/math] of [math]\displaystyle{ G }[/math] and [math]\displaystyle{ G^{\ast} }[/math], respectively, are mathcalled geometric duals if an edge of [math]\displaystyle{ \Gamma }[/math] crosses the corresponding edge of [math]\displaystyle{ \Gamma^{\ast} }[/math] and intersects no other edges of [math]\displaystyle{ \Gamma^{\ast} }[/math]. It follows that the vertices of [math]\displaystyle{ \Gamma }[/math] and [math]\displaystyle{ \Gamma^{\ast} }[/math] are in a one-to-one correspondence with the faces of [math]\displaystyle{ \Gamma^{\ast} }[/math] and [math]\displaystyle{ \Gamma }[/math], respectively.