Here's a picture of an irregular tetrahedron, for reference: The base triangle (ABC) is completely known (lengths AB, AC, BC, and the angles between them are all known). The 3 angles at vertex P are also known (APB, APC, and BPC). I believe that is enough information to completely solve the rest of the lengths and angles. I used the law of sines and the 180 degree constraint for each of the 3 unknown triangles. With a bit of algebra I can get 3 equations with 3 unknowns, but they're too messy for me to solve. If anyone can figure this out, I'd greatly appreciate it.