 Point-line duality

A point $[a:b:c]$ of the projective plane corresponds to the dual line $aX+bY+cZ=0$. A line given by those coefficients corresponds back to the point $[a:b:c]$. Incidence is reversed: $p\in \ell$ if and only if ${\ell }^{\ast }\in p^{\ast }$. Thus collinear point triples become concurrent line triples, preserving the essential combinatorics of incidence geometry.