A regular octahedron can be used as a "tile" for various puzzle; we find it when we put together 4 polyhedra of this kind, as we can see with the mirrors.
By putting together an octahedron and four regular tetrahedra, we get another regular tetrahedron with double edge: this proves that the volume of an octahedron is 4 times the volume of a tetrahedron with the same edge.
You can see also a net.
The image belongs to the sections...:
Models of polyhedra (3D geometry)
Octahedron (3D geometry)
Puzzles involving reconstruction of polyhedra (3D geometry)