A number of attractive 5-compounds of the regular icosahedron can be constructed.
The compounds illustrated above are implemented in the Wolfram Language as PolyhedronData[
"IcosahedronFiveCompound",
n
]
for 
,
2, 3.
These icosahedron 5-compounds are illustrated above together with their dodecahedron 5-compound duals and common midspheres.
The common solids and convex hulls are illustrated above.
