Editing Symmedian (section)

==Tetrahedra==
The concept of a symmedian point extends to (irregular) tetrahedra. Given a tetrahedron {{mvar|ABCD}} two planes {{mvar|P, Q}} through {{mvar|AB}} are isogonal conjugates if they form equal angles with the planes {{mvar|ABC}} and {{mvar|ABD}}. Let {{mvar|M}} be the midpoint of the side {{mvar|{{overline|CD}}}}. The plane containing the side {{mvar|{{overline|AB}}}} that is isogonal to the plane {{mvar|ABM}} is called a symmedian plane of the tetrahedron. The symmedian planes can be shown to intersect at a point, the symmedian point. This is also the point that minimizes the squared distance from the faces of the tetrahedron.<ref name="SBR">{{citation|first1=Jawad|last1=Sadek|first2=Majid|last2=Bani-Yaghoub|first3=Noah|last3=Rhee|title=Isogonal Conjugates in a Tetrahedron|journal=Forum Geometricorum
|volume=16|pages=43–50|year=2016|url=http://forumgeom.fau.edu/FG2016volume16/FG201606.pdf}}.</ref>