A number of attractive 12-compounds of the regular tetrahedron can be constructed.
The compounds illustrated above are implemented in the Wolfram Language as PolyhedronData[
"TetrahedronTwelveCompound",
n
]
for 
,
2.
These tetrahedron 12-compounds are illustrated above together with their duals and common midspheres.
The common solids and convex hulls are illustrated above. The convex hull of the first is a polyhedral
realization of graph 
in Li et al. (2023; E. Weisstein, Sep. 28, 2023).
The interior of the second has the connectivity of the disdyakis
dodecahedron and its convex hull has the connectivity
of the great rhombicuboctahedron.
