# Projective plane

From Groupprops

Template:Incidence structure property

## Contents

## Definition

### Symbol-free definition

A **projective plane** is an incidence structure satisfying the following properties (note that blocks are now called *line*s):

- To any two distinct points, there is a unique line incident with both of them
- To any two distinct lines, there is a unique point incident with both of them
- There exist four points of which no three are incident with the same line

A set of four points as described by the third condition is termed a *quadrangle*. Note that conditions (1) and (2) are dual to each other, and further, that these, along with (3), also imply the existence of *quadrilateral*s which are the dual notion to quadrangles.

A projective plane can also be viewed as a square 2-design with .