Jawad Sadek, Majid Bani-Yaghoub, and Noah. H. Rhee,
Isogonal conjugates in a tetrahedron,
Forum Geometricorum, 16 (2016) 43--50.
Abstract. The symmedian point of a tetrahedron is defined and the existence of the symmedian point of a tetrahedron is proved through a geometrical argument. It is also shown that the symmedian point and the least squares point of a tetrahedron are concurrent. We also show that the symmedian point of a tetrahedron coincides with the centroid of the corresponding pedal tetrahedron. Furthermore, the notion of isogonal conjugate to tetrahedra is introduced, with a simple formula in barycentric coordinates. In particular, the barycentric coordinates for the symmedian point of a tetrahedron are given.
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