There are a number of attractive polyhedron compounds consisting of two octahedra. The first (left figure) consists of two octahedra rotated
above a common 
symmetry axes. The second (middle figure) consists of two octahedra rotated above
a common 
symmetry axes.
These compounds are implemented in the Wolfram Language as PolyhedronData[
"OctahedronTwoCompound",
n] for 
,
2, 3.
These octahedron 2-compounds are illustrated above together with their cube 2-compound duals and common midspheres.
The common solids and convex hulls of these compounds are illustrated above.
The net for the 
octahedron 2-compound is illustrated above. For octahedra with unit edge lengths,
the side lengths are
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
The surface area of the compound is
 |
(4)
|
