\begin{definition}[Definition:Fano Plane]
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.
:400px
\end{definition}