A self-dual configuration is a configuration that is isomorphic to its dual, with the roles of points and lines interchanged. Equivalently, its Levi graph has a graph automorphism that interchanges the two classes of its bipartition.
More explicitly, a duality pairs every point 
with a line 
and every line 
with a point 
so that 
lies on 
if and only if 
lies on 
. Thus the pairing reverses the roles of points and lines
while preserving the incidence relation.
Some self-dual configurations are summarized below (Coxeter 1950, Grünbaum 2009).
For example, realize the points of the Desargues configuration as the two-element subsets of 
and its lines as the three-element subsets, with
incidence given by containment. Sending each subset to its complement exchanges points
and lines and gives an explicit self-duality.
