Duality in projective geometry

Summary

In a projective plane, points and lines play symmetric roles: two points lie on one line, and two lines meet in one point. Duality is the exchange of the words "point" and "line", together with "lies on" and "passes through". The principle of duality says that the dual of a theorem valid in all projective planes is again a theorem valid in all projective planes. In a projective space of dimension $n$, duality exchanges subspaces of dimension $d$ and $n - 1 - d$.