I've got an irregular solid with a vertex at which three faces (and thus also 3 edges) come together. None of the angles involved are right angles. I know the angles of the corners, at that vertex, of the three faces. I need to find the angle between two of the faces (in a plane perpendicular to their shared edge; the plane of the third face isn't perpendicular, so I can't just use its corner angle).

What is the formula to relate the three face-corner angles to the angle between two of the faces?

Edit: I want this because I'm trying to fabricate an irregularly-shaped box to fit into a constrained space. I have college mathematics, including geometry, and calculus-based geometry, but excluding whatever spherical geometry is.