# Quadrangle, complete

From Encyclopedia of Mathematics

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.

#### Comments

#### 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) |

**How to Cite This Entry:**

Quadrangle, complete.

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

This article was adapted from an original article by P.S. ModenovA.S. Parkhomenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article