\begin{definition}[Definition:Finite Projective Plane/Order 4]
The finite projective plane of order $4$.
It can be denoted:
:$\operatorname {PG} \left({4, 4}\right)$
where:
:$\operatorname {PG}$ stands for '''projective geometry'''
:the first parameter $2$ specifies the dimension
:the second parameter $2$ specifies the order.
$\operatorname {PG} \left({4, 4}\right)$ has the following properties:
: It has $21$ points
: It has $21$ lines
: There are $5$ points on each line
: There are $5$ lines through each point.
\end{definition}