Complete quadrangle

In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four points in a plane, no three of which are on a common line, and of the six lines connecting the six pairs of points.

The complete quadrilateral has also been called a Pasch configuration, especially in the context of Steiner triple systems.

Due to the discovery of the Fano plane, a finite geometry in which the diagonal points of a complete quadrangle are collinear, some authors have augmented the axioms of projective geometry with Fano's axiom that the diagonal points are not collinear,[2] while others have been less restrictive.

The four points on the line deriving from the sides and diagonals of the quadrangle are called a harmonic range.

Developments of modern geometry and algebra note the influence of von Staudt on Mario Pieri and Felix Klein .