Theorem of Dihedral Angles
The dihedral angle of a regular tetrahedron and the dihedral angle of a regular octahedron are supplementary.
A constructive solution employs one (regular) octahedron and 4
(regular) tetrahedra, all having the same side lengths.
Paste the tetrahedra onto the octahedron, such that each pair of tetrahedra shares no edge.