A Theorem on the Dihedral Angles of a Tetrahedron
Let , , , , , be the edges of a tetrahedron and let , , , , , be the corresponding dihedral angles. Define the function on pairs of opposite edges and dihedral angles as , where is the dihedral angle at and is the dihedral angle at .[more]
A theorem states that this function is constant on the three pairs of opposite edges of a tetrahedron.[less]
The proof can be found in [1, p. 101, p. 113].
 V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.