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A Theorem on the Dihedral Angles of a Tetrahedron

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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 .

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A theorem states that this function is constant on the three pairs of opposite edges of a tetrahedron.

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Contributed by: Izidor Hafner (February 2017)
Open content licensed under CC BY-NC-SA

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Details

The proof can be found in [1, p. 101, p. 113].

Reference

[1] V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.

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