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  "body": "\n## Summary\n\nAn embedding of a graph in a surface is a drawing of the graph on the surface in which edges meet only at shared ends.\nEmbeddings in the plane or sphere are the subject of planar graph theory, and embeddings in other surfaces lead to the genus of a graph.\nMany results, such as [[Euler's formula|0W1C598HMS]] and the notion of a [[dual graph|1QHTD1DS5J]], are statements about embedded graphs.\n\n## Explanations\n\n### L1 human\n\nTo embed a graph is to draw it on a surface with no two edges crossing.\nSome graphs, like $K_5$, cannot be drawn on a sheet of paper without crossings, but they can be drawn on the surface of a doughnut.\nThe genus of a graph measures how many handles a surface needs before the graph fits on it.\n",
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