n + 1 points at each edge of a tetrahedron
Source: Rioplatense 1995 L3 P3
September 19, 2022
geometry3D geometrycombinatoricstetrahedroncombinatorial geometry
Problem Statement
Given a regular tetrahedron with edge , its edges are divided into equal segments, thus obtaining points: at the ends and 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 that belong (simultaneously) to four planes of that set are considered. Determine the smallest positive natural so that among those points the eight vertices of a square-based rectangular parallelepiped can be chosen.