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.
The common solids and convex hulls are illustrated above. For the first compound, the interior has the connectivity of a tetrakis hexahedron and the convex hull has the connectivity of the truncated octahedron. For the second, the interior is a 12-dipyramid and the convex hull is a (non-equilateral) 12-prism. For the third, the interior is a truncated 9-trapezohedron (with the connectivity of the -generalized Petersen graph) and the convex hull is a gyroelongated 9-dipyramid.
A net for the hull of the first compound is illustrated above, with
(1)
| |||
(2)
| |||
(3)
| |||
(4)
| |||
(5)
| |||
(6)
| |||
(7)
|