Can one calculate trihedral angles from 3 normals? Clearly you can for the normals define the orientation of the planes bounding the angle. If x and y are unit normals to the two n−1 spaces of a dihedral angle then that angle is cos⁻¹ (− x ⋅ y). Given three unit normals for a trihedral angle, compute the three dihedral angles αⁿ₂, by pairs and then αⁿ₃ = ∑αⁿ₂ − π. This works for it is valid in the 3 space spanned by the 3 unit normals. It is the ancient area formula for spherical triangles.