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.).
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.
|[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)|
Quadrangle, complete. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadrangle,_complete&oldid=17067