Symmedian point of a triangle and a tetrahedron

We present the symmedian point of a triangle which is one of several thousand particular points associated to a triangle. First the isogonal conjugate of a line through a vertex of the triangle is defined in order to define the symmedian point. We take a closer look at some of the interesting properties of the symmedian point of a triangle and the relationship of the symmedian point with some other particular points of the triangle. Next we consider a tetrahedron and define the isogonal conjugate of a plane through a side of the tetrahedron. This enables us to define the symmedian planes of any tetrahedron. A proof that all six symmedian planes of a tetrahedron intersect in a common point is presented and this point is called the symmedian point of the tetrahedron