# Determining a tetrahedron from 2 faces and a 1 dihedral angle [closed]

If I know 2 faces of a tetrahedron (that is, 5 edge lengths in total as the 2 faces share 1 edge), and 1 dihedral angle, how can I determine the 6th edge?
Is the 6th edge always unique?

Does it matter which dihedral angle I know?
For instance, can I uniquely determine the tetrahedron if the 1 dihedral angle I know is along the last (i.e. the 6th unknown) edge?

Thanks for any insight.

• Do you know about vectors and how they add componentwise in euclidean space? Commented Aug 1 at 14:52
• @SammyBlack, I do. I know dihedral angles are related to the normals to the faces. But I’m not certain how to derive this last edge length and whether it is always unqiue. Commented Aug 1 at 15:02
• You're going to have uniqueness issues if you only know the edge lengths (as sets of size $3$, overlapping in one place) and the angle. You can flip one of the triangles, swapping vertices that it shares with the other, and get a different tetrahedron (different sixth edge). However, if you specify particular configuration of edges, then the resulting tetrahedron should be unique up to congruence. Commented Aug 1 at 15:06
• So you have two triangles linked by a common side. If you know the angle between these two triangles, your shape is fixed. Otherwise I don't think it's unique. Commented Aug 1 at 15:11