rectangular parallelepiped
Source: French MO 1996 P3
April 11, 2021
3D geometrygeometry
Problem Statement
(a) Let there be given a rectangular parallelepiped. Show that some four of its vertices determine a tetrahedron whose all faces are right triangles.
(b) Conversely, prove that every tetrahedron whose all faces are right triangles can be obtained by selecting four vertices of a rectangular parallelepiped.
(c) Now investigate such tetrahedra which also have at least two isosceles faces. Given the length of the shortest edge, compute the lengths of the other edges.