Complete quadrangle
= Complete quadrangle
{title2=$4\text{ vertices},\quad6\text{ joining lines}$}
A complete quadrangle consists of four <projective points> in the <projective plane>, no three collinear, and all six joining <projective lines>. Its three diagonal points are the intersections of opposite joining lines. Over a <field> of characteristic different from two, the line joining two diagonal points cuts either side through the third diagonal point in a pair of <harmonic conjugate points>. In a <projective frame> this follows by using the coordinate points and $[1:1:1]$ and computing the intersections.