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.