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Construct a Dihedral Angle of a Tetrahedron Given Its Plane Angles at a Vertex

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Given the tetrahedron , at the vertex let be the three plane angles , , . This Demonstration constructs the dihedral angle at the edge .

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Construct the tetrahedron from the original tetrahedron by modifying the lengths of the sides starting at : cut off by the plane orthogonal to the edge at the vertex . The dihedral angle along is the angle at vertex of the triangle .

Given the edge length of and the angles , the other edges are given by: , , , , . It helps to construct the net of .

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

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The problem was posed in [1, pp. 222].

Reference

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

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