Sines of the Dihedral Angles of a Tetrahedron

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Let be a tetrahedron with dihedral angles , , , , , . A theorem relating the sines of the dihedral angles states that .


Here , and are pairs of opposite edges of the tetrahedron.


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



A proof is described in [1, pp. 111].


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

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