Given a regular tetrahedron with edge a, its edges are divided into n equal segments, thus obtaining n+1 points: 2 at the ends and n−1 inside. The following set of planes is considered:
∙ those that contain the faces of the tetrahedron, and
∙ each of the planes parallel to a face of the tetrahedron and containing at least one of the points determined above.
Now all those points P that belong (simultaneously) to four planes of that set are considered. Determine the smallest positive natural n so that among those points P the eight vertices of a square-based rectangular parallelepiped can be chosen. geometry3D geometrycombinatoricstetrahedroncombinatorial geometry