The negated dihedral angle of the octahedron differs from the angle of a tetrahedron by an integer multiple of , and in addition the octahedron has two times as many edges as the tetrahedron (twelve instead of six). Therefore, the Dehn invariant of the octahedron is −2 times the Dehn invariant of a tetrahedron of the same edge length. The Dehn invariants of the other Archimedean solids can also be expressed as rational combinations of the invariants of the Platonic solids.