Dihedral angle along an edge between two half-planes
DihedralAngle[{p1, p2}, {v, w}]
DihedralAngle[{{0, 0, 0}, {0, 1, 0}}, {{1, 0, 1}, {1, 0, 0}}]
→ Pi/4DihedralAngle[{{0, 1, 0}, {0, 0, 0}}, {{1, 0, 1}, {1, 0, 0}}]
→ Pi/4DihedralAngle[{{0, 1, 0}, {0, 0, 0}}, {{a, b, c}, {1, 0, 0}}]
→ ArcCos[a/Sqrt[Abs[a]^2 + Abs[c]^2]]