A number of attractive 11-compounds of the regular icosahedron can be constructed.

The compound illustrated above is implemented in the Wolfram Language as `PolyhedronData`[`"IcosahedronElevenCompound"`,
1].

This icosahedron 11-compound is illustrated above together with its dodecahedron 11-compound dual and common midsphere.

The common solid and convex hull, the former of which has the connectivity of the truncated octahedron, are illustrated above.