A number of attractive 6-compounds of the regular icosahedron can be constructed.
The compounds illustrated above are implemented in the Wolfram Language as PolyhedronData[
"IcosahedronSixCompound",
n
]
for 
,
2.
This icosahedron 6-compound is illustrated above together with its dodecahedron 6-compound duals and common midspheres.
The common solids and convex hulls are illustrated above.
