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  "body": "\n## Summary\n\nA Schlegel diagram is a picture of a $d$-dimensional [[convex polytope|300K6CB1KH]] inside one of its [[facets|DPDXN2FJC4]], one dimension lower.\nIt is obtained by looking at the polytope from a point just outside that facet and projecting the rest of the boundary onto it.\nThe result is a subdivision of the facet into convex polytopes, one for each other facet, that keeps the full face structure.\nSchlegel diagrams make $4$-dimensional polytopes visible in space and give a quick proof that graphs of $3$-polytopes are [[planar|0NC9R64TXP]].\n\n## Explanations\n\n### L1 human\n\nPut your eye very close to one face of a cube and look through it.\nYou see the far face as a small square inside the near one, joined to it by the four side faces seen as trapezoids.\nThat drawing, a square inside a square with the corners joined, is the Schlegel diagram of the cube.\nThe same trick shows a four-dimensional cube as a small cube inside a big cube, with six squashed cubes in between.\n",
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