a tetrahedron is divided into five polyhedra
Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1997 p3
February 20, 2020
combinatorial geometry3D geometrygeometry
Problem Statement
A tetrahedron is divided into five polyhedra so that each face of the tetrahedron is a face of (exactly) one polyhedron, and that the intersection of any two of the polyhedra is either a common vertex, a common edge, or a common face. What is the smallest possible sum of the numbers of faces of the five polyhedra?