Monge point

Summary

The Monge point of a tetrahedron is the common point of six planes. Each of them passes through the midpoint of an edge and is perpendicular to the opposite edge. It is the reflection of the circumcentre in the centroid. It plays the role in a tetrahedron that the orthocentre plays in a triangle, because the altitudes of a tetrahedron need not meet. The definition extends to every simplex of dimension at least $2$, and for a triangle it gives the orthocentre.