---
tag: FGKNAFNHA3
kind: concept
name: Incidence structure
msc: [51A05, 05B25]
sources:
  - url: https://en.wikipedia.org/wiki/Incidence_structure
same_as:
  wikidata: Q367329
  wikipedia: Incidence structure
---

## Summary

An incidence structure consists of a set of points, a set of lines, and a relation that says which points lie on which lines.
Nothing else is assumed: there are no distances, no angles and no coordinates.
Projective planes, affine planes, block designs and many other combinatorial objects are incidence structures with extra axioms.
It is the basic object of [[incidence geometry|CSXT0BG2CM]].

## Explanations

### L1 human

Take some dots and some curves, and record only which dots sit on which curves.
That record is an incidence structure.
For example, take the $7$ points and $7$ lines of the Fano plane, where each line has $3$ points and each point is on $3$ lines.
Exchanging the roles of points and lines gives the dual structure, which is again an incidence structure.