Definition:Fano Plane

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

It can be denoted:

$\operatorname {PG} \left({2, 2}\right)$


$\operatorname {PG}$ 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.


Also see

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

Source of Name

This entry was named for Gino Fano.