Interior dihedral angle of a convex polyhedron ($\cos \theta =-{\hat{\mathbf{n}}}_1\cdot {\hat{\mathbf{n}}}_2$)

At an edge of a convex polyhedron, its interior dihedral angle is the angle of the wedge inside the solid, measured in a plane perpendicular to the edge. If the two incident faces have outward unit normal vectors ${\hat{\mathbf{n}}}_1,{\hat{\mathbf{n}}}_2$, then their normal angle is supplementary to the interior angle. Thus $\cos \theta =-{\hat{\mathbf{n}}}_1\cdot {\hat{\mathbf{n}}}_2$. Equivalently, subtract from each vector pointing into one face its orthogonal projection onto the common edge; the angle between the resulting inward face directions is the interior angle. This distinguishes an interior angle from the acute angle convention for two unoriented planes.