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  "body": "\n## Summary\n\nIn a [[projective plane|DANFNN8C4Y]], points and lines play symmetric roles: two points lie on one line, and two lines meet in one point.\nDuality is the exchange of the words \"point\" and \"line\", together with \"lies on\" and \"passes through\".\nThe principle of duality says that the dual of a theorem valid in all projective planes is again a theorem valid in all projective planes.\nIn a projective space of dimension $n$, duality exchanges subspaces of dimension $d$ and $n - 1 - d$.\n\n## Explanations\n\n### L1 human\n\nTake any true statement about points and lines of the projective plane and swap the two words.\n\"Two points determine a line\" becomes \"two lines determine a point\", which is also true in the projective plane.\nSo every theorem comes with a free twin.\nFor example, [[Pascal's theorem|94AKWRHND0]] about six points on a conic has [[Brianchon's theorem|3THE3Q96KK]] about six lines tangent to a conic as its dual twin.\n",
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