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  "body": "\n## Summary\n\nThe dual graph of a graph drawn in the plane has one vertex for each face of the drawing.\nIt has one edge for each edge of the drawing, joining the two faces on its two sides.\nDuality exchanges faces and vertices, and cycles and minimal cuts.\nIt depends on the chosen [[embedding|CG91WNMG2T]], not only on the abstract graph, and the same idea works for graphs embedded in other surfaces.\n\n## Explanations\n\n### L1 human\n\nThink of a map of countries.\nPut a capital in each country, and join two capitals by a road crossing each stretch of border that the two countries share.\nThe road network is the dual graph of the map of borders.\nFor example, the dual of the graph of a cube, which has $6$ faces, is the graph of an octahedron, which has $6$ vertices.\n",
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