PlaneDual returns the plane dual of a planar graph G, that is, a graph with faces of G as its vertices in which two vertices are adjacent if and only if they share an edge as faces of G.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$\mathrm{DrawGraph}\left(\mathrm{HypercubeGraph}\left(3\right)\,\mathrm{style}=\mathrm{spring}\right)$

$G≔\mathrm{PlaneDual}\left(\mathrm{HypercubeGraph}\left(3\right)\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 6\; vertices\; and\; 12\; edge(s)}$

$\mathrm{DrawGraph}\left(G\,\mathrm{style}=\mathrm{spring}\right)$