Construct a Dihedral Angle of a Tetrahedron Given Its Plane Angles at a Vertex
Given the tetrahedron , at the vertex let be the three plane angles , , . This Demonstration constructs the dihedral angle at the edge .[more]
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 .[less]
The problem was posed in [1, pp. 222].
 V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.