Tetrahedron 12-compounds can be constructed in a number of attractive forms.
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. E. Weisstein observed on Sep. 28, 2023, that the convex hull of
the first is a polyhedral realization of the graph denoted 
by Li et al. (2026). The interior of the second
has the connectivity of the disdyakis dodecahedron
and its convex hull has the connectivity of the great rhombicuboctahedron.
