The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a complete graph. The only simple polyhedron with no diagonals is the tetrahedron. The only known toroidal polyhedron with no diagonals is the Császár polyhedron.

Császár polyhedron | Euler brick | polygon diagonal | polyhedron | space diagonal | tetrahedron