A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella
octangula. A second can be obtained by arranging six regular tetrahedra about
a common
copies. A third can be obtained by combining two oppositely-oriented tetrahedron
3-compounds.

These tetrahedron 6-compounds are illustrated above together with their duals
and common midspheres.

Hart, G. "Compound of Six Tetrahedra." http://www.georgehart.com/virtual-polyhedra/vrml/compound_of_six_tetrahedra.wrl.Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica.
Püspökladány, Hungary: Uniconstant, p. 129, 2002.Skilling,
J. "Uniform Compounds of Uniform Polyhedra." Math. Proc. Cambridge Phil.
Soc.79, 447-457, 1976.