A number of attractive 8-compounds of the regular tetrahedron can be constructed.
The compounds illustrated above are implemented in the Wolfram Language as PolyhedronData[
"TetrahedronEightCompound",
n
]
for 
,
..., 4.
These tetrahedron 8-compounds are illustrated above together with their duals and common midspheres.
The common solids and convex hulls are illustrated above.
