Isogonal conjugation in isosceles tetrahedron

2026/01/29 by Saro Harutyunyan · 1 voice
Mathematics · #math.HO #math.MG

paper · pdf

Abstract

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.

Citations

• Coincidences of simplex centers and related facial structures
• The Geometry of an Equifacetal Simplex

Discussions

• Saro Harutyunyan: Isogonal conjugation in isosceles tetrahedron https://arxiv.org/abs/2601.22042 https://arxiv.org/pdf/2601.22042 https://arxiv.org/html/2601.22042 [bsky, 0 points, 0 comments]

Related

• Constructions in the Locus of Isogonal Conjugates in a Quadrilateral
• Miquel point and isogonal conjugation
• Isogonal Conjugacy and Fermat Problems
• Extreme Points on Circumconics Induced by Isogonal Conjugates in a Triangle
• A One-Line Proof of Leversha's "Quartet of Isogonal Conjugates" Theorem