Cutting a convex polyhedron into pieces
Source: 239 2013 S6
August 7, 2020
geometry
Problem Statement
Convex polyhedron with triangular faces is cut into tetrahedrons; all the vertices of the tetrahedrons are the vertices of the polyhedron, and any two tetrahedrons either do not intersect, or they intersect along a common vertex, common edge, or common face. Prove that it it's not possible that each tetrahedron has exactly one face on the surface of .