Quadrangle, complete

A collection of four points (lying in a plane), no three of which lie on the same line, and the six lines connecting these points (cf. Fig.).

Figure: q076010a

The points are called the vertices, and the lines are called the edges of the complete quadrangle. Edges that have no common vertex are called opposite; the points of intersection of the opposite edges are called diagonal points.

If and are the points of intersection of the line with the lines and , then the four points form a harmonic quadruple of points. The dual figure to a quadrangle is called a quadrilateral — a collection of four lines (in a plane), no three of which contain a common point.

References

[a1]	H.S.M. Coxeter, "Projective geometry" , Springer (1987) pp. 7; 95
[a2]	H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)
[a3]	M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)