Editing Incidence structure (section)

==Dual structure==

If we interchange the role of "points" and "lines" in
<math display="block">C = (P, L, I)</math>
we obtain the ''dual structure'',
<math display="block">C^* = (L, P, I^*)</math>
where {{math|''I''<sup>∗</sup>}} is the [[converse relation]] of {{mvar|I}}. It follows immediately from the definition that:
<math display="block">C^{**} = C</math>

This is an abstract version of [[Duality (projective geometry)|projective duality]].<ref name=Demb1 />

A structure {{mvar|C}} that is [[isomorphic]] to its dual {{math|''C''<sup>∗</sup>}} is called ''self-dual''. The Fano plane above is a self-dual incidence structure.