Upside-Down

In this problem, you are given a tetrahedron in 333-dimensional space. A tetrahedron is defined as “a solid having four plane triangular faces; a triangular pyramid.” You are given the coordinates of 4 vertices of a tetrahedron in 333-dimensional space. It is guaranteed that the first 333 out of 444 of these points are situated in a plane parallel to the XYXYXY plane. Let’s call this plane the base of the tetrahedron. Let’s call the 4th point the apex of this tetrahedron. It is also guaranteed that the center of mass of this tetrahedron is the origin of this coordinate system.


This is a companion discussion topic for the original entry at https://toph.co/p/upside-down