Isogonal conjugation in isosceles tetrahedron

In this article we investigate the properties of isogonal conjugation in isosceles tetrahedron. Particularly we reveal three hyperbolic paraboloids each of which is formed by pairs of isogonal conjugate points symmetric in the respective bimedian, as well as we prove that the circumsphere of an isosceles tetrahedron is invariant under isogonal conjugation in that tetrahedron.