A planar straight line embedding of a planar graph is a planar embedding in which only straight line segments are used to connect the graph vertices. Fáry showed that every planar graph has a planar straight line embedding with noncrossing edges, and such embeddings (with rectilinear crossing number 0) are sometimes known as a Fáry embedding. A planar straight line embedding of a planar graph can be constructed in the Wolfram Language using the PlanarEmbedding option to GraphLayout or in the Wolfram Language using PlanarGraph[g].
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