Definition:Fano Plane

Definition
The Fano plane is the finite projective plane of order $2$.

It can be denoted:
 * $\operatorname {PG} \left({2, 2}\right)$

where:
 * $\operatorname {PG}$ stands for projective geometry
 * the first parameter $2$ specifies the dimension
 * the second parameter $2$ specifies the order.

$\operatorname {PG} \left({2, 2}\right)$ has the following properties:
 * It has $7$ points
 * It has $7$ lines
 * There are $3$ points on each line
 * There are $3$ lines through each point.


 * FanoPlane.png

Also see
From Structure of Fano Plane, $\operatorname {PG} \left({2, 2}\right)$ has the fewest points and lines.