Editing Discrete geometry (section)

===Incidence structures===
{{main|Incidence structure}}
[[File:Fano plane with nimber labels.svg|thumb|right|150px|Seven points are elements of seven lines in the [[Fano plane]], an example of an incidence structure.]]

Incidence structures generalize planes (such as [[affine plane (incidence geometry)|affine]], [[projective plane|projective]], and [[Möbius plane]]s) as can be seen from their axiomatic definitions. Incidence structures also generalize the higher-dimensional analogs and the finite structures are sometimes called [[Finite geometry|finite geometries]].

Formally, an '''incidence structure''' is a triple
:<math>C=(P,L,I).\,</math>

where ''P'' is a set of "points", ''L'' is a set of "lines" and <math>I \subseteq P \times L</math> is the [[Incidence (geometry)|incidence]] relation. The elements of <math>I</math> are called '''flags.''' If
:<math>(p,l) \in I,</math>

we say that point ''p'' "lies on" line <math>l</math>.

Topics in this area include:
*[[Configuration (geometry)|Configurations]]
*[[Arrangement of lines|Line arrangements]]
*[[Arrangement of hyperplanes|Hyperplane arrangements]]
*[[Building (mathematics)|Buildings]]