Pappus configuration

Example

The Pappus configuration is a configuration $(9_3)$ in the projective plane. Take distinct points $A, B, C$ on a line $g$ and distinct points $a, b, c$ on another line $h$, none of them on both lines. Let $X = Ab \cap aB$, $Y = Ac \cap aC$ and $Z = Bc \cap bC$. By Pappus's hexagon theorem, $X$, $Y$, $Z$ lie on a line, the Pappus line.

Its $9$ points are $A, B, C, a, b, c, X, Y, Z$. Its $9$ lines are $g$, $h$, the six lines $Ab$, $aB$, $Ac$, $aC$, $Bc$, $bC$ and the Pappus line. Check: each line has $3$ of the points, for instance $Ab$ contains $A$, $b$, $X$ and $Bc$ contains $B$, $c$, $Z$. Each point lies on $3$ lines. For instance, $A$ lies on $g$, $Ab$, $Ac$, the point $b$ on $h$, $Ab$, $bC$, and $X$ on $Ab$, $aB$ and the Pappus line. Its incidence graph is the Pappus graph.