The four planes determined by the four altitudes of a tetrahedron and the orthocenters of the corresponding faces pass through the Monge point of the tetrahedron.
Mannheim's Theorem
See also
Monge Point, TetrahedronExplore with Wolfram|Alpha
References
Altshiller-Court, N. "The Monge Point." §4.2c in Modern Pure Solid Geometry. New York: Chelsea, pp. 69-71, 1979.Mannheim, A. J. de math. élémentaires, p. 225, 1895.Thompson, H. F. "A Geometrical Proof of a Theorem Connected with the Tetrahedron." Proc. Edinburgh Math. Soc. 17, 51-53, 1908-1909.Referenced on Wolfram|Alpha
Mannheim's TheoremCite this as:
Weisstein, Eric W. "Mannheim's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MannheimsTheorem.html